Question

Solve: $3x+4y=10$ and $2x-2y=2$

Answer 1

Step 1: Finding the expression for $x$ from equation $\left(1\right)$

The given equations are as follows

$$\begin{gathered} 3x+4y=10............\left(1\right) \\ 2x-2y=2..............\left(2\right) \end{gathered}$$

From equation $\left(1\right)$, $x=\frac{10-4y}{3}....................\left(3\right)$

Step 2: Finding the value of $y$ by putting the value of $x$ in equatrion $\left(2\right)$

Put $x=\frac{10-4y}{3}$ in equation $\left(2\right)$, we get

$\Rightarrow 2\times \frac{\left(10-4y\right)}{3}-2y=2$

$$\begin{gathered} \Rightarrow \frac{20-8y}{3}-2y=2 \\ \Rightarrow \frac{20-8y-6y}{3}=2 \\ \Rightarrow 20-14y=6 \end{gathered}$$

$\Rightarrow 14y=14$

$\Rightarrow y=1$

Step 3: Putting the value of $y$ in equation $\left(3\right)$

On putting $y=1$ in $x=\frac{10-4y}{3}$, we get

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

Hence, $x=2$ and $y=1$ is the correct answer.