Question

Solve $2x-y=5$ and $3x+2y=11$ by substitution.

Answer 1

Substitution method:

The given two equations are

$$\begin{gathered} 2x–y=5\dots ..\left(I\right) \\ 3x+2y=11\dots .\left(II\right) \end{gathered}$$

Multiplying $\left(I\right)$ with $2$ we get

$4x–2y=10\dots .\left(III\right)$

Adding $\left(II\right)$ with $\left(III\right)$

$$\begin{gathered} 7x=21 \\ x=3 \end{gathered}$$

Putting the value of$x$ in $\left(I\right)$ we get

$$\begin{gathered} 2\times 3-y=5 \\ \Rightarrow 6-y=5 \\ \Rightarrow y=1 \end{gathered}$$

Hence, $x=3$ and $y=1$is the correct answer.