Question

Solve the following equations by substitution method:

$5x-2y=13;4x+3y=15$

• A. $x=1,y=-3$
• B. $x=3,y=1$
• C. $x=-1,y=3$
• D. $x=-1,y=-3$

Answer 1

The correct option is B $x=3,y=1$

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

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

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

Substitute the value of $x$ in equation $4x+3y=15$. We get

$4\left(\frac{13+2y}{5}\right)+3y=15\Rightarrow 52+8y+15y=75\Rightarrow 23y=23\Rightarrow y=1$

Therefore, $y=1$

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

$5x-2=13$

$5x=13+2=15$

$x=3$

Hence, the solution is $x=3,y=1$.