Question

$$\begin{gathered} 2x-\frac{3y}{4}=3, \\ 5x=2y+7. \end{gathered}$$

Answer 1

The given equations are:
$2x-\frac{3y}{4}=3$ ........(i)
5x = 2y + 7 ............(ii)

On multiplying (i) by 2 and (ii) by $\frac{3}{4}$, we get:
$4x-\frac{3}{2}y=6$ .......(iii)
$\frac{15}{4}x=\frac{3}{2}y+\frac{21}{4}$ .......(iv)

On subtracting (iii) from (iv), we get:
$$\begin{gathered} -\frac{1}{4}x=-\frac{3}{4} \\ \Rightarrow x=3 \end{gathered}$$

On substituting x = 3 in (i), we get:
$$\begin{gathered} 2\times 3-\frac{3y}{4}=3 \\ \Rightarrow \frac{3y}{4}=(6-3)=3 \\ \Rightarrow y=\frac{3\times 4}{3}=4 \end{gathered}$$

Hence, the solution is x = 3 and y = 4.