Question

Solve the simultaneous equations using elimination method.
$7x+2y=12$
$2x-17y=25$

• A. $(\frac{109}{51},-\frac{151}{102})$
• B. $(-\frac{151}{102},\frac{109}{51})$

Answer 1

The correct option is A $(\frac{109}{51},-\frac{151}{102})$

The given equations are:
$7x+2y=12...\left(a\right)$
$2x-14y=25...\left(b\right)$

To eliminate $x,$ multiply equation $\left(a\right)$ by $2,$ and equation $\left(b\right)$ by $7.$

$[7x+2y=12]\times 2$
$\Rightarrow 14x+4y=24...\left(c\right)$

$[2x-14y=25]\times 7$
$\Rightarrow 14x-98y=175...\left(d\right)$

Now, substract $\left(d\right)$ from $\left(c\right).$

(14x+4y)-(14x-98y)=24-175
$\Rightarrow 14x+4y-14x+98y=-151$
$\Rightarrow 102y=-151$
$\Rightarrow y=-\frac{151}{102}$

Substituting value of $y$ in $\left(a\right)$ we get,
$7x+2(-\frac{151}{102})=12$
$\Rightarrow 7x-\frac{151}{51}=12$
$\Rightarrow 7x=12+\frac{151}{51}$
$\Rightarrow 7x=\frac{51\times 12+151}{51}$
$\Rightarrow 7x=\frac{763}{51}$
$\Rightarrow x=\frac{109}{51}$

$\therefore$ $(\frac{109}{51},-\frac{151}{102})$ is the solution.