Answer
The solution to this system of equations is $a = -1$ and $b = 3$.
Work Step by Step
We see that in the two equations, the $a$ term is the exactly the same except they have opposite signs.
If we add these two equations together, we can eliminate the variable $a$ and just deal with one variable instead of two:
$(3a+4b) +(-3a-2b)3=9+(-3)\\
2b=6$
Divide each side by $2$ to solve for $b$:
$b = 3$
Now that we have the value for $b$, we can plug it into one of the equations to solve for $a$.
Let us plug the value for $b$ into the first equation:
$3a + 4(3) = 9$
$3a + 12 = 9$
Now, we subtract $12$ from both sides of the equation to isolate constants to the right side of the equation:
$3a = -3$
Divide both sides by $3$ to solve for $a$:
$a = -1$
The solution to this system of equations is $a = -1$ and $b = 3$.
