Question

Solve the following simultaneous equations:

$8x+13y-29=0$, $12x-7y-17=0$

• A. $x=3;y=2$
• B. $x=0;y=5$
• C. $x=2;y=1$
• D. $x=-1;y=3$

Answer 1

The correct option is C $x=2;y=1$

We pick either of the equations and write one variable in terms of the other.

Let us consider the equation $8x+13y=29$ and write it as

$x=\frac{29-13y}{8}.........\left(1\right)$

Substitute the value of $x$ in Equation $12x-7y=17$. We get

$12\left(\frac{29-13y}{8}\right)-7y=17\Rightarrow 87-39y-14y=34\Rightarrow 87-53y=34\Rightarrow -53y=-53\Rightarrow y=1$

Therefore, $y=1$

Substituting this value of $y$ in Equation (1), we get

$x=\frac{29-13}{8}=\frac{16}{8}=2$

Hence, the solution is $x=2,y=1$.