3x-5y=4 and 9x-2y=7. Solve this simultaneous linear equation by substitution method. [ICSE ML Aggarwal Class 9 Chapter 5 Exercise 5.1 Question Number 1(iv) Solution]
3x-5y=4 —-(i)
9x-2y=7 —-(ii)
From equation (i) we get,
3x = 4+5y
$\Rightarrow x = \frac{4 + 5y}{3}$ —-(iii)
Substituting the value of x in equation (ii) we get,
$9\left(\frac{4 + 5y}{3}\right)$ – 2y = 7
⟹ 3(4+5y)-2y=7
⟹ 12+15y-2y=7
⟹ 12+13y=7
⟹ 13y=7-12
⟹ 13y=-5
⟹ y=$-\frac{5}{13}$
From equation (iii) we get,
${\mathrm{x}}$ = $\frac{4 + 5\left(\frac{ – 5}{13}\right)}{3}$
$\Rightarrow {\mathrm{x}}$ = $\frac{52 – 25}{39}$
$\Rightarrow {\mathrm{x}}$ = $\frac{27}{39}$
$\Rightarrow {\mathrm{x}}$ = $\frac{9}{13}$
Therefore Required Solutions are x =$\frac{9}{13}$ and y=$-\frac{5}{13}$