Question

Solve the equations using elimination method:
$5a-6b=2$ and $6a-5b=9$

• A. (4, -3)
• B. (-4, 3)
• C. (4, 3)
• D. (-4, -3)

Answer 1

The correct option is C (4, 3)

$5a-6b=2$ ----- (1)
$6a-5b=9$ ----- (2)
Multiply equation (1) by 6 and equation (2) by 5, and then subtract the equation (3) and (4)
$30a-36b=12$ ----- (3)
$30a-25b=45$ ----- (4)
(-) (+) (-)
______________
$-11b=-33$
$b=\frac{-33}{-11}=3$
Put the value of b in equation (1), we get
$5a-6b=2$
$5a-6\left(3\right)=2$
$5a=2+18$
$a=\frac{20}{5}=4$
Therefore the solution is (4, 3)