Question

8x-3y=5xy,6x-5y=-2xy. How to solve it using elimination method

Answer 1

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Answer 2

Answer:

In elimination method we solve a system of two linear equations of two variables by eliminating one variable after operating the equations,

Given equations,

8x-3y=5xy,

$\implies \frac{8}{y}-\frac{3}{x}=5----(1)$

6x-5y=-2xy

$\implies \frac{6}{y}-\frac{5}{x}=-2----(2)$

∵ LCM(8, 6) = 24,

3 × equation (1) - 4 × equation (2),

We get,

$-\frac{9}{x}+\frac{20}{x}=15 + 8$

$\frac{-9+20}{x}=23$

$\frac{11}{x}=23$

$\implies x = \frac{11}{23}$

From equation (1),

$\frac{8}{y}-\frac{69}{11}=5$

$\frac{8}{y}=5+\frac{69}{11}$

$\frac{8}{y}=\frac{55+69}{11}$

$\frac{8}{y}=\frac{124}{11}$

$\implies y = \frac{88}{124}=\frac{22}{31}$