Question

Solve the following equations using substitution method:
$2x+3y=13$ and $4x+5y=23$

• A. (-2, 3)
• B. (2, 3)
• C. (2, -3)
• D. (-2, -3)

Answer 1

The correct option is B (2, 3)

Given: $2x+3y=13$ ------(1)
$4x+5y=23$ ------(2)

From equation (1),
$2x+3y=13$
$y=\frac{13-2x}{3}$

Substitute the value of $y$ in equation (2):
$4x+5y=23$
$4x+5\left(\frac{13-2x}{3}\right)=23$
$12x+65-10x=69$
$2x=69-65$
$2x=4$
$x=2$

Then substitute the value of $x$ in equation (1):
$2\left(2\right)+3y=13$
$4+3y=13$
$3y=13-4$
$3y=9$
$y=3$
Therefore solution is $x=2$ ans $y=3$