Question

Solve: $3x+4y=25$,$5x-6y=-9$ by elemination method.

Answer 1

Given :

$$\begin{gathered} 3x+4y=25\dots \dots \dots ..\left(1\right) \\ 5x–6y=-9\dots \dots \dots \dots \left(2\right) \end{gathered}$$

Multiplying equation $\left(1\right)$ by $3$ and equation $\left(2\right)$ by $2$

$$\begin{gathered} 9x+12y=75\dots .\left(3\right) \\ 10x–12y=-18\dots ..\left(4\right) \end{gathered}$$

On solving equations $\left(3\right)$and $\left(4\right)$, we get,

$$\begin{gathered} 19x=57 \\ x=57/19 \\ x=3 \end{gathered}$$

Now,

Substitute$x=3$in equation $\left(2\right)$

$$\begin{gathered} 5\left(3\right)–6y=-9 \\ 15–6y=-9 \\ 6y=15+9 \\ 6y=24 \\ y=24/6 \\ y=4 \end{gathered}$$

Therefore, $x=3$ and $y=4$