Question

Without plotting the graph, find the point of intersection of the lines $2x+5y=13$ and $4x-9y=7$.

• A. $(8,2)$
• B. $(7,-5)$
• C. $(4,1)$
• D. $(-2,4)$

Answer 1

The correct option is C $(4,1)$

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

Let us consider the equation $2x+5y=13$ and write it as

$x=\frac{13-5y}{2}$

Substitute the value of $x$ in equation $4x-9y=7$. We get

$4\left(\frac{13-5y}{2}\right)-9y=7\Rightarrow 26-10y-9y=7\Rightarrow -19y=-19\Rightarrow y=1$

Therefore, $y=1$

Substituting this value of $y$ in the equation $2x+5y=13$, we get

$2x+5=13$

$2x=13-5=8$

$x=4$

Hence, the point of intersection is $(4,1)$.