Question

Solve the following pairs of linear equations by elimination method:

$78x+91y=39$ and $65x+117y=42$

• A. $x=\frac{3}{13},y=\frac{3}{13}$
• B. $x=\frac{1}{11},y=\frac{2}{11}$
• C. $x=\frac{5}{17},y=\frac{4}{17}$
• D. Cannot be determined

Answer 1

The correct option is A $x=\frac{3}{13},y=\frac{3}{13}$

Given system of equations are:
$78x+91y=39...\left(1\right)$
$65x+117y=42...\left(2\right)$
Now using elimination method will first eliminate $x$ .
now multiplying eq $\left(1\right)$ by $65$ and eq $\left(2\right)$ by $-78$.
$\Rightarrow \left(65\right)78x+\left(65\right)91y=\left(65\right)39$
$\Rightarrow (-78)65x+\left(78\right)117y=\left(65\right)42$
$\Rightarrow 5070x+5915y=2535...\left(3\right)$
$\Rightarrow -5070x-9126y=-3276...\left(4\right)$
From equation $\left(3\right)$ and $\left(4\right)$, we get
$-3211y=-741$
$\Rightarrow y=\frac{-741}{-3211}$
$y=\frac{3}{13}$
Now substituting $y=\frac{3}{13}$ in eq $\left(1\right)$
$\Rightarrow 78x+91\left(\frac{3}{13}\right)=39$
$\Rightarrow 1014x+273=507$
$\Rightarrow 1014x=507-273$
$\Rightarrow 1014x=234$
$\Rightarrow x=\frac{234}{1014}$
$\Rightarrow x=\frac{3}{13}$
$\Rightarrow x=\frac{3}{13},y=\frac{3}{13}$