Question

Solve by using elimination method:

$3x+4y=10and2x-2y=2$

Answer 1

Step 1: Find the value of $x$.

Given :

$$\begin{gathered} 3x+4y=10...................\left(i\right) \\ 2x-2y=2....................\left(ii\right) \end{gathered}$$

Multiply (ii) by $2$

$4x-4y=4...............\left(iii\right)$

Add equation (i) and (iii) we get

$$\begin{gathered} 7x=14 \\ \Rightarrow x=\frac{14}{7} \\ \Rightarrow x=2 \end{gathered}$$

Step 2: Find the value of $y$

Put $x=2$ in equation (i) we get

$$\begin{gathered} 3\times 2+4y=10 \\ \Rightarrow 6+4y=10 \\ \Rightarrow 4y=10-6 \\ \Rightarrow 4y=4 \\ \Rightarrow y=1 \end{gathered}$$

Hence, The solution of the given equation is $x=2,y=1$