Question

One month Tammy rented

Answer 1

$3x + 2y = 20$
$8x + 4y = 45$
$where x = # of movies$ and $y = # of video games$

In order to solve this systems of equations problem, you need to use the elimination method.

You can multiply the top equation, $3x + 2y = 20$, by -2 in order to eliminate the $y$ values.

$(3x + 2y = 20) *-2$ will turn into $-6x - 4y = -40$

From there, we can eliminate.

$-6x - 4y = -40$
$8x + 4y = 45$

Since $4y$ and $-4y$ are opposites in sign and equal in coefficients, we can remove them from our equations and add the rest of the terms together.

$-6x - 4y = -40$
$8x + 4y = 45$
will turn into -->
$2x = 5$

So, x = $\frac{5}{2}$, which means 1 movie costs $2.50. Then, we can solve for the video game price, $y$, by substituting our x back into one of the equations.

$3x + 2y = 20$
$3*\frac{5}{2} + 2y = 20$
$y = \frac{25}{4}$

Each movie costs $2.50 and each video game costs $6.25.