Answer
$x = 6$
$y = 0$
Work Step by Step
To solve a system of equations using substitution, we plug in an expression in place of a variable. In this system of equations, we already have one variable expressed in terms of the other variable, so let's use the second equation to substitute for $y$ in the first equation:
$4x + 9(-\frac{1}{3}x + 2) = 24$
Use the distributive property on the right side of the equation:
$4x - \frac{9}{3}x + 18 = 24$
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, $3$:
$4x - 3x + 18 = 24$
Combine like terms on the left side of the equation:
$x + 18 = 24$
Subtract $18$ from each side of the equation to move constants to the right side of the equation:
$x = 6$
Now that we have the value for $x$, we can substitute it into one of the equations to solve for $y$:
$y = (-\frac{1}{3})(6) + 2$
Multiply first:
$y = -\frac{6}{3} + 2$
Simplify the fraction by dividing the numerator and denominator by their greatest common factor, $3$:
$y = -2 + 2$
Add to solve for $y$:
$y = 0$
