Question

Solve the following pair of equations using cross multiplication method [2 MARKS]

x + 2y = -2 , x - y = 4

Answer 1

Concept : 1 Mark
Calculation : 1 Mark

Given equations are,

$x+2y=-2,\Rightarrow x+2y+2=0\dots \dots \left(i\right)$

Comparing this equation with $a_{1}x+b_{1}y+c_1=0$, we get
$a_1=1,b_1=2,c_1=2$

$x-y=4,\Rightarrow x-y-4=0\dots \dots \left(ii\right)$

Comparing this equation with $a_{2}x+b_{2}y+c_2=0$, we get
$a_2=1,b_2=-1,c_2=-4$

From cross multiplication method, we have,
$x=\frac{b_1{c}_2-b_2{c}_1}{a_1{b}_2-a_2{b}_1}$ , $y=\frac{c_1{a}_2-c_2{a}_1}{a_1{b}_2-a_2{b}_1}$

$x=\frac{\left[\right(2\left)\right(-4)-(-1\left)\right(2\left)\right]}{\left(1\right)(-1)-\left(1\right)\left(2\right)}$

$x=\frac{\left[\right(-8)-(2\left)\right]}{(-1)-\left(2\right)}$

$\Rightarrow x=2$

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

$y=\frac{\left[\right(2\left)\right(1)-(-4\left)\right(1\left)\right]}{\left(1\right)(-1)-\left(1\right)\left(2\right)}$

$y=\frac{\left[\right(2)-(-4\left)\right]}{(-1)-\left(2\right)}$

$\Rightarrow y=-2$

$\therefore$ $x=2$ , $y=-2$