Question

# Solve the following simultaneous equation:$x + y = 8 \\ 3x + 4y = 25 \\$

Hint: Find the value of one variable in the form of the other variable from the first equation. Then put it in the second equation.

$x + y = 8 .....(i) \\ 3x + 4y = 25 .....(ii) \\$
From equation $(i)$, we have:
$\Rightarrow x + y = 8, \\ \Rightarrow x = 8 - y \\$
Putting this value in equation $(ii)$, we’ll get:
$\Rightarrow 3\left( {8 - y} \right) + 4y = 25, \\ \Rightarrow 24 - 3y + 4y = 25, \\ \Rightarrow y = 1 \\$
Putting $y = 1$ in equation $(i)$, we’ll get:
$\Rightarrow x + 1 = 8, \\ \Rightarrow x = 7 \\$
Thus, the solution of the simultaneous equation is $x = 7$ and $y = 1$.