\(3x + 2y = 20\)
\(8x + 4y = 45\)
\(where x = # of movies\) 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, @@MATH_TOKEN_16@@, by substituting our x back into one of the equations.
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Each movie costs $2.50 and each video game costs $6.25.
