Question

Solve the following simultaneous linear equations using the substitution method.
$5y=27x+8;100y-200x-704=0$

x-coordinate is

y-coordinate is

Answer 1

We need to solve
$5y=27x+8...\left(a\right)$
$100y-200x-704=0...\left(b\right)$

Expressing $\left(a\right)$ in terms of $x$ we get,
$y=\frac{27x+8}{5}$

Substituting $y$ in $\left(b\right)$ we get,
$100y-200x-704=0$
$\Rightarrow 100\left(\frac{27x+8}{5}\right)-200x-704=0$
$\Rightarrow 20(27x+8)-200x-704=0$
$\Rightarrow 540x+160-200x-704=0$
$\Rightarrow 340x-544=0$
$\Rightarrow x=\frac{544}{340}$
$\Rightarrow x=1.6$

Substituting $x$ in (a) we get,
$y=\frac{27x+8}{5}$
$\Rightarrow y=\frac{27\left(1.6\right)+8}{5}$
$\Rightarrow y=\frac{43.2+8}{5}$
$\Rightarrow y=10.24$