Question

Solve the following simultaneous equations:
$\frac{1}{4}x+y=11;x+\frac{1}{5}y=6$

Answer 1

Given equations: $\frac{1}{4}x+y=11;x+\frac{1}{5}y=6$ can be simplified as
$x+4y=44$ ---- eq. (i) and $5x+y=30$---- eq. (ii)

Multiplying eq. (ii) with $4$, we get,
$4(5x+y)=4\times 30$
$⟹20x+4y=120$ ---- eq. (iii)

Now, subtracting eq. (i) from eq. (iii), we get,
$⟹20x+4y-(x+4y)=120-44$
$⟹20x+4y-x-4y=76$
$⟹19x=76$
$⟹x=4$

Now, substituting $x=4$ in eq. (ii), we get,
$⟹5x+y=30$
$⟹5\left(4\right)+y=30$
$⟹20+y=30$
$⟹y=10$

$\therefore x=4$ and $y=10$ is the solution for the given pair of linear equations.