II technikum

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To się liczy! 2. Reforma 2019

Pierwszy układ równań: {2x+y=−12x−y=9​ &nbsp; {y=−2x−1−y=−2x+9 ∣⋅(−1)​ &nbsp; {y=−2x−1y=2x−9​ &nbsp; &nbsp; <table style="border-collapse: collapse;width: 100%;" border="1"> <tbody> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> x &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> 0 &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> 3 &nbsp;&nbsp;</td> </tr> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> y=−2x−1 &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> −1 &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> −7 &nbsp;&nbsp;</td> </tr> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> y=2x−9 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> −9 &nbsp;&nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> −3 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td> </tr> </tbody> </table> &nbsp;

{x−y=0−x+y=2​ &nbsp; &nbsp; Przekształćmy oba równania do postaci&nbsp; y=ax+b &nbsp;:

a) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e6b344b37cc84b69a7444c719f72a36b664cab68389674871396586ec657ba4d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e6b344b37cc84b69a7444c719f72a36b664cab68389674871396586ec657ba4d_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/51939e7ff51c2a0777008f7abd5f777b7e3fbc88213e079079cb5deb437a3e35_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/51939e7ff51c2a0777008f7abd5f777b7e3fbc88213e079079cb5deb437a3e35_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4ffbe94b16072e2136355c44bf4f72f5e9f3731e04819fd8df66ff7c145a2bfa_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4ffbe94b16072e2136355c44bf4f72f5e9f3731e04819fd8df66ff7c145a2bfa_big.svg" type="image/svg+xml"></object> &nbsp; &nbsp; <table style="border-collapse: collapse;width: 100%;" border="1"> <tbody> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/fe3116220ced3b1141beba12b41bece15d7792544164de1200ee4917fbae67d4_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/fe3116220ced3b1141beba12b41bece15d7792544164de1200ee4917fbae67d4_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/615bdd17c2556f82f384392ea8557f8cc88b03501c759e23093ab0b2a9b5cd48_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/615bdd17c2556f82f384392ea8557f8cc88b03501c759e23093ab0b2a9b5cd48_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> </tr> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b327feb42a9fe07a5b4a5d84aa1ddbf9906eff60b2d9df71926a42f0b8adcda5_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b327feb42a9fe07a5b4a5d84aa1ddbf9906eff60b2d9df71926a42f0b8adcda5_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/ef2d127de37b942baad06145e54b0c619a1f22327b2ebbcfbec78f5564afe39d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/ef2d127de37b942baad06145e54b0c619a1f22327b2ebbcfbec78f5564afe39d_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/2c624232cdd221771294dfbb310aca000a0df6ac8b66b696d90ef06fdefb64a3_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/2c624232cdd221771294dfbb310aca000a0df6ac8b66b696d90ef06fdefb64a3_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> </tr> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/3dfe5ce297a5073c04bd7a95e973f38ee9b7fb4c37613f1bc9ac1a3a439f18f6_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/3dfe5ce297a5073c04bd7a95e973f38ee9b7fb4c37613f1bc9ac1a3a439f18f6_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;&nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/19581e27de7ced00ff1ce50b2047e7a567c76b1cbaebabe5ef03f7c3017bb5b7_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/19581e27de7ced00ff1ce50b2047e7a567c76b1cbaebabe5ef03f7c3017bb5b7_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;&nbsp;</td> </tr> </tbody> </table> &nbsp; <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/120602/zg5s5OblFWdhx/8CXgh59w%3D%3D_fbd4d410daaf00ef5b4bb627248bc950e7a52d969bb2995772d31fd386513621.jpg" alt="" width="637" height="544"> Podstawa trójkąta ma długość: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/9c02d789749d023c04b7016618095cb1be42bbaeb5608c1ce3f5ff750514a21a_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/9c02d789749d023c04b7016618095cb1be42bbaeb5608c1ce3f5ff750514a21a_big.svg" type="image/svg+xml"></object> &nbsp; Wysokość: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/59583f7dafcc4f976e37fb9073a9bf59156c567ba6559c207ab0e2c6db4ea90e_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/59583f7dafcc4f976e37fb9073a9bf59156c567ba6559c207ab0e2c6db4ea90e_big.svg" type="image/svg+xml"></object> &nbsp; Pole:&nbsp;&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/0fb241bcf75577185eb2aeeef7d684984dddd7d0b83e92d3a9b4c4e36bd09b0d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/0fb241bcf75577185eb2aeeef7d684984dddd7d0b83e92d3a9b4c4e36bd09b0d_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; <hr> b) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e1cf857549deb6c8dc6d7723f1b98ea4fff930d64b39de3ff3132195cd5ec056_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e1cf857549deb6c8dc6d7723f1b98ea4fff930d64b39de3ff3132195cd5ec056_big.svg" type="image/svg+xml"></object> &nbsp; &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/346015f144828f513fc88b0173c24889a20fc25fb65e917095f1b7a01b2cb050_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/346015f144828f513fc88b0173c24889a20fc25fb65e917095f1b7a01b2cb050_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;

Pierwszy układ równań: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/6f6c9faec1c340bb9be650b516842e8355592b9d23bc9800d01c68cf5b02840b_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/6f6c9faec1c340bb9be650b516842e8355592b9d23bc9800d01c68cf5b02840b_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/d50b8f62a30d934e656ca1186038be3de312f364eff163bee1e6a321b2b1245a_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/d50b8f62a30d934e656ca1186038be3de312f364eff163bee1e6a321b2b1245a_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e676df8698c590af4f8d6394af2406f06880a27bc752b6c44c9e81e34c570faa_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e676df8698c590af4f8d6394af2406f06880a27bc752b6c44c9e81e34c570faa_big.svg" type="image/svg+xml"></object> &nbsp; &nbsp; <table style="border-collapse: collapse;width: 100%;" border="1"> <tbody> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/fe3116220ced3b1141beba12b41bece15d7792544164de1200ee4917fbae67d4_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/fe3116220ced3b1141beba12b41bece15d7792544164de1200ee4917fbae67d4_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4e07408562bedb8b60ce05c1decfe3ad16b72230967de01f640b7e4729b49fce_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4e07408562bedb8b60ce05c1decfe3ad16b72230967de01f640b7e4729b49fce_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> </tr> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c5c4f9237cc619de90672e14bf7c17511b9c2689b22ca645396e02876dcbf44e_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c5c4f9237cc619de90672e14bf7c17511b9c2689b22ca645396e02876dcbf44e_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/1bad6b8cf97131fceab8543e81f7757195fbb1d36b376ee994ad1cf17699c464_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/1bad6b8cf97131fceab8543e81f7757195fbb1d36b376ee994ad1cf17699c464_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/a770d3270c9dcdedf12ed9fd70444f7c8a95c26cae3cae9bd867499090a2f14b_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/a770d3270c9dcdedf12ed9fd70444f7c8a95c26cae3cae9bd867499090a2f14b_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;</td> </tr> <tr> <td style="background-color: #dbdbdb;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/51126ca8de5d946e65bbfa68ee879a5d9ed43b4ba06ebed1b385aa810f0b0ab8_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/51126ca8de5d946e65bbfa68ee879a5d9ed43b4ba06ebed1b385aa810f0b0ab8_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/d5c534fde62beb89c745a59952c8efed8b7523cbd047e682782e4367de9ea3bf_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/d5c534fde62beb89c745a59952c8efed8b7523cbd047e682782e4367de9ea3bf_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;&nbsp;</td> <td style="width: 33.3333%;text-align: center;vertical-align: middle;"> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/615bdd17c2556f82f384392ea8557f8cc88b03501c759e23093ab0b2a9b5cd48_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/615bdd17c2556f82f384392ea8557f8cc88b03501c759e23093ab0b2a9b5cd48_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td> </tr> </tbody> </table> &nbsp;

$x$	$0$	$3$
$y = - 2 x - 1$	$- 1$	$- 7$
$y = 2 x - 9$	$- 9$	$- 3$

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