Question

Choose the correct answer which satisfies the linear equations: $-5a+9b=-12$ and $3a+2b=22$

• A. ($6,2)$
• B. $(6,-2)$
• C. $(-6,-2)$
• D. $(-6,2)$

Answer 1

The correct option is A ($6,2)$

$-5a+9b=-12$ ----- (1)
$3a+2b=22$ ----- (2)
Substitute the values of first option $a=6$ and $b=2$ in equations 1 and 2
$-5a+9b=-12$
$-5\left(6\right)+9\left(2\right)=-12$
$-30+18=-12$
$-12=-12$
$3a+2b=22$
$3\left(6\right)+2\left(2\right)=22$
$18+4=22$
$22=22$
Therefore, the first option satisfied the linear equations.
Likewise substitute the value of second option $a=6,b=-2$
$-5a+9b=-12$
$-5\left(6\right)+9(-2)=-12$
$-30-18=-12$
$-48\ne -12$
$3a+2b=22$
$3\left(6\right)+2(-2)=22$
$18-4=22$
$14\ne 22$
Similarly, check the options to satisfy the linear equation.
Here, the first option satisfied the linear equation.
The solution is $(6,2)$