Question

Solve the following sets of simultaneous equations.

$$\begin{gathered} 2x+3y+4=0 \\ x-5y=11 \end{gathered}$$

Answer 1

Given:

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

and$x–5y=11\dots \left(2\right)$

Multiplying equation $\left(2\right)$ by $2$, we obtain

$2x–10y=22\dots \left(3\right)$

Subtracting equation $\left(3\right)$ from equation $\left(1\right)$, we obtain

$$\begin{gathered} 2x+3y-2x+10y=-4-22 \\ \Rightarrow 13y=-26 \\ \Rightarrow y=\frac{-26}{13} \\ \Rightarrow y=-2 \end{gathered}$$

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

$$\begin{gathered} 2x+3(-2)=-4 \\ \Rightarrow 2x–6=-4 \\ \Rightarrow 2x=2 \\ \Rightarrow x=1 \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}$ and $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2}$ are the solution of given pair of equation.