Question

If $\frac{x}{4}+\frac{y}{3}=\frac{5}{12}\mathrm{and}\frac{x}{2}+y=1$, then find the value of (x + y).

Answer 1

The given pair of equations is
$$\begin{gathered} \frac{x}{4}+\frac{y}{3}=\frac{5}{12}.....\left(i\right) \\ \frac{x}{2}+y=1.....\left(ii\right) \end{gathered}$$
Multiplying (i) by 12 and (ii) by 4, we get
$$\begin{gathered} 3x+4y=5.....\left(iii\right) \\ 2x+4y=4.....\left(iv\right) \end{gathered}$$
Now, subtracting (iv) from (iii), we get
$x=1$
Putting x = 1 in (iv), we have
$$\begin{gathered} 2+4y=4 \\ \Rightarrow 4y=2 \\ \Rightarrow y=\frac{1}{2} \end{gathered}$$
$\therefore x+y=1+\frac{1}{2}=\frac{3}{2}$
Hence, the value of x + y is $\frac{3}{2}$.