Question

Solve the following pair of equations by cross multiplication rule.

$ax+by+a=0,bx+ay+b=0$

• A. $x=-9,y=1$
• B. $x=-1,y=0$
• C. $x=1,y=-1$
• D. $x=6,y=-2$

Answer 1

The correct option is B $x=-1,y=0$

Given systems of equations are:
$ax+by+a=0$
$bx+ay+b=0$

To solve $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ this pair of equations

for x and y using cross-multiplication,
$x=\frac{b_1{c}_2-b_2{c}_1}{a_1{b}_2-a_2{b}_1}$

$y=\frac{c_1{a}_2-c_2{a}_1}{a_1{b}_2-a_2{b}_1}$

now put the values from given equations,

$\Rightarrow x=\frac{b\left(b\right)-a\left(a\right)}{(a\times a)-(b\times b)}$

$\Rightarrow y=\frac{a\left(b\right)-b\left(a\right)}{(a\times a)-(b\times b)}$

$\Rightarrow x=\frac{b^2-a^2}{a^2-b^2}$

$\Rightarrow x=-1$

$\Rightarrow y=\frac{ab-ba}{a^2-b^2}$

$\Rightarrow y=0$