Question

Find the solution of the following pair of equations using cross multiplictaion [2 MARKS]

$2x+y=5$

$3x+2y=8$

Answer 1

Concept : 1 Mark
Calculation : 1 Mark

Given equations are,

$2x+y=5\Rightarrow 2x+y-5=0\dots \dots \left(i\right)$

$a_1=2,b_1=1,c_1=-5$

$3x+2y=8\Rightarrow 3x+2y–8=0\dots \dots \left(ii\right)$

$a_2=3,b_2=2,c_2=-8$

$x=\frac{b_1{c}_2-b_2{c}_1}{a_1{b}_2-a_2{b}_1}$

$x=\frac{\left[\right(1\left)\right(-8)-(2\left)\right(-5\left)\right]}{\left(2\right)\left(2\right)-\left(3\right)\left(1\right)}$

$x=\frac{\left[\right(-8)-(-10\left)\right]}{\left(4\right)-\left(3\right)}$

$\Rightarrow x=2$

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

$y=\frac{\left[\right(-5\left)\right(3)-(-8\left)\right(2\left)\right]}{\left(2\right)\left(2\right)-\left(3\right)\left(1\right)}$

$y=\frac{\left[\right(-15)-(-16\left)\right]}{\left(4\right)-\left(3\right)}$

$\Rightarrow y=1$