Question

Solve the following pair of linear equations by the elimination method

$$\begin{gathered} 3x-5y-4=0 \\ 9x=2y+7 \end{gathered}$$

Answer 1

Step 1: Find the value of one variable by modifying equations and subtracting them.

Given pair of equations are:

$$\begin{gathered} 3x-5y-4=0 \\ \Rightarrow 3x-5y=4.....\left(1\right) \\ 9x=2y+7 \\ \Rightarrow 9x-2y=7.......\left(2\right) \end{gathered}$$

Multiply equation $\left(1\right)$ by $3$, we get

$9x-15y=12......\left(3\right)$

Subtracting equation $\left(2\right)$ from equation $\left(3\right)$, we get,

$$\begin{gathered} 9x-15y-9x+2y=12-7 \\ \Rightarrow -13y=5 \\ \Rightarrow y=\frac{-5}{13} \end{gathered}$$

Step 2: Find the value of $x$.

Put the value of $y$ in equation $\left(1\right)$, we get

$$\begin{gathered} 3x-5\left(\frac{-5}{13}\right)=4 \\ \Rightarrow 3x+\frac{25}{13}=4 \\ \Rightarrow 3x=4-\frac{25}{13} \\ \Rightarrow 3x=\frac{52-25}{13} \\ \Rightarrow x=\frac{27}{13\times 3} \\ \Rightarrow x=\frac{9}{13} \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{9}}{\mathbf{13}}$ and $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{-}\mathbf{5}}{\mathbf{13}}$ are the solutions of given pair of linear equation.