Question

2x + 3y = 7 : (a-b)x + (a+b)y = 3a + b - 2 step by step explanation ​

Answer 1

Answer:

$\mathcal{x=\frac{2(a-2b-3)}{a-5b}} \\ \\ \mathcal{y=\frac{a-9b+4}{a-5b}}$

Step-by-step explanation:

$\huge\mathcal{Given}</p><p>\\</p><p>2x+3y=7 ======>\bold{EQ\:01}</p><p>\\</p><p>(a\:-\:b)x+(a+b)y=3a+b\:-\:2====>\bold{EQ\:02}</p><p>\\</p><p>Apply</p><p>\\</p><p>\left[(\bold{EQ\:01})\times(a\:-\:b)\right]\:-\:[(\bold{EQ\:02})\times2]</p><p>\\</p><p>==>\:\:2.(a-b).x\:\:\:\:\:+3(a-b).y\:\:\:\:\:\:\:\:=7(a-b)</p><p>\\</p><p>==>-[2.(a\:-\:b)x+2.(a+b)y=2.3a+2.b\:-\:2.2]</p><p>\\</p><p>==>\:\:\:0\:\:\:\:\:\:\:\:+3(a-b)y-2y(a+b)=7a-7b-6a-2b+4</p><p>\\</p><p>(3a-3b-2a-2b)y=a-9b+4</p><p>\\</p><p>(a\:-\:5b)y=a-9b+4</p><p>\\</p><p>\huge\mathcal{y=\frac{a-9b+4}{a-5b}}</p><p>\\</p><p>substitute \:y\:value\:in\:(EQ\:01)</p><p>\\</p><p>2x+3\left(\frac{a-9b+4}{a-5b}\right)=7</p><p>\\</p><p>2x=7-3\left(\frac{a-9b+4}{a-5b}\right)</p><p>\\</p><p>2x=\frac{7a-35b-3a+27b-12}{a-5b}</p><p>\\</p><p>2x=\frac{4a-8b-12}{a-5b}</p><p>\\</p><p>\huge\mathcal{x=\frac{2(a-2b-3)}{a-5b}}$

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