Answer
$a = 3$, $b = 2$, or $(3,2)$
Work Step by Step
Given:
$2a + 3b = 12$
$5a - b = 13$
Multiply both sides of the second equation by $3$ to get an equivalent equation:
$15a - 3b = 39$
Add the equations, $2a + 3b = 12$, and $15a - 3b = 39$:
$2a + 3b + (15a - 3b) = 12 + (39)
\\2a + 3b + 15a - 3b = 12 + 39$
Combine like terms:
$17a = 51$
Divide both sides by $17$:
$a = 3$
Substitute $a = 3$ back into first equation, $2a + 3b = 12$ :
$2(3) + 3b = 12
\\6 + 3b = 12$
Subtract $6$ from both sides:
$3b = 6$
Divide both sides by $3$:
$b = 2$
Thus, $a = 3$, $b = 2$
