Question

ax+by=a+b/2 , 3x+ 5y= 4 solve this equation for x and y

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$x = \frac{(3b-5a)}{(6b-10a)}$

$y =\frac{(3b-5a)}{(6b-10a)}$

Step-by-step explanation:

$Given \\ ax+by=\frac{a+b}{2}$

$\implies 2ax+2by=a+b--(1)$

$and\\3x+5y=4 ---(2)$

Multiply equation (1) by 3 ,and equation (2) by 2a , we get

6ax+6by=3a+3b ---(3)

6ax+10ay = 8a -----(4)

Subtract equation (4) from equation (3), we get

(6b-10a)y = 3a+3b-8a

=> (6b-10a)y = 3b-5a

$\implies y = \frac{3b-5a}{6b-10a}--(5)$

$Now, \\Substitute \:value \: of \: y\\ \: in \: equation \: (2), \: we \: get$

$3x+\frac{5(3b-5a)}{6b-10a}=4$

$\implies 3x = 4 -\frac{5(3b-5a)}{6b-10a}$

$\implies 3x = 4 -\frac{15b-25a)}{6b-10a}$

$\implies 3x = \frac{24b-40a-15b+25a}{6b-10a}$

$\implies 3x=\frac{9b-15a}{6b-10a}$

$\implies x = \frac{3(3b-5a)}{3(6b-10a)}$

$\implies x = \frac{(3b-5a)}{(6b-10a)}---(6)$

Therefore,

$x = \frac{(3b-5a)}{(6b-10a)}$

$y =\frac{(3b-5a)}{(6b-10a)}$

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