Answer
The solution to this system of equations is $(3, 0)$.
Work Step by Step
We need to modify one equation so that one of the variables is the same in both equations but differing in sign. Let's multiply the second equation by $-4$:
$-8x - 4y = -24$
Now, we set up the system of equations using the first equation and the modified equation:
$3x + 4y = 9$
$-8x - 4y = -24$
Combine the two equations by adding them together:
$-5x = -15$
Divide both sides of the equation by $-5$:
$x = 3$
Substitute this value for $x$ into one of the equations to solve for $y$:
$2(3) + y = 6$
Multiply first:
$6 + y = 6$
Subtract $6$ from both sides of the equation:
$y = 0$
The solution to this system of equations is $(3, 0)$.
