Question

Question 3
Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x +5y = 9
3x +2y = 4

Answer 1

8x +5y = 9 ... (i)
3x +2y = 4 ... (ii)

Compare the given equations with

$a_{1}x+b_{1}y+c_1=0and{a}_{2}x+b_{2}y+c_2=0$.

Substitution method

From equation (ii), we get
$x=\frac{4-2y}{3}$ ... (iii)
Putting this value in equation (i), we get
$8\times \frac{4-2y}{3}+5y=9$
$\Rightarrow 32-16y+15y=27$
$\Rightarrow -y=-5$
$\Rightarrow y=5...\left(iv\right)$
Substituting this value in equation (ii), we get

$3x+10=4$
$\Rightarrow x=-2$
Hence, x = -2, y = 5

Cross multiplication method

8x + 5y -9 = 0
3x + 2y - 4 = 0

$\frac{x}{b_1{c}_2-b_2{c}_1}=\frac{y}{c_1{a}_2-c_2{a}_1}=\frac{1}{a_1{b}_2-a_2{b}_1}$
$\frac{x}{-20-(-18)}=\frac{y}{-27-(-32)}=\frac{1}{16-15}$
$\frac{x}{-2}=\frac{y}{5}=\frac{1}{1}$
$\frac{x}{-2}=1$ and $\frac{y}{5}=1$
$x=-2andy=5$