Question

Solve by substitution method:

$3x+4y=10,2x-2y=2$

Answer 1

By substitution method,

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

Substituting $x=y+1$ in other equation

$$\begin{gathered} \Rightarrow 3x+4y=10 \\ \Rightarrow 3\left(y+1\right)+4y=10 \\ \Rightarrow 3y+3+4y=10 \\ \Rightarrow 7y=10-3 \\ \Rightarrow 7y=7 \\ \Rightarrow y=1 \end{gathered}$$

$x=y+1\Rightarrow x=1+1\Rightarrow x=2$

Hence, the value of $x=2,y=1$.