Accuplacer Advanced Algebra and Functions Practice Exam

To find the solution to the system of equations \(2x + 3y = 6\) and \(4x - y = 5\), we can solve it using the method of substitution or elimination.

First, let's express \(y\) from the first equation. Rearranging \(2x + 3y = 6\) gives:

\[3y = 6 - 2x\]

Dividing everything by 3:

\[y = 2 - \frac{2}{3}x\]

Next, we substitute this expression for \(y\) into the second equation \(4x - y = 5\). Substituting gives:

\[4x - \left(2 - \frac{2}{3}x\right) = 5\]

This simplifies to:

\[4x - 2 + \frac{2}{3}x = 5\]

Combining like terms, we convert \(4x\) to a fraction:

\(\frac{12}{3}x - 2 + \frac{2}{3}x = 5\)

Adding the fractions results in:

\[\left(\frac{12 + 2}{3}\