Question

4x + 2y = 16\
-4x + 5y = 12

Explanation:

Step1: Add the two equations to eliminate \(x\)

We have the system of equations:
\[

$$\begin{cases} 4x + 2y = 16 \\ -4x + 5y = 12 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations respectively:
\((4x + 2y)+(-4x + 5y)=16 + 12\)
Simplify the left - hand side: \(4x-4x+2y + 5y=7y\), and the right - hand side: \(28\). So we get the equation \(7y=28\).

Step2: Solve for \(y\)

From \(7y = 28\), divide both sides of the equation by \(7\):
\(y=\frac{28}{7}=4\)

Step3: Substitute \(y = 4\) into one of the original equations to solve for \(x\)

We substitute \(y = 4\) into the first equation \(4x+2y = 16\).
We get \(4x+2\times4=16\), that is \(4x + 8=16\).
Subtract \(8\) from both sides: \(4x=16 - 8=8\).
Divide both sides by \(4\): \(x=\frac{8}{4}=2\)

Answer:

The solution of the system of equations is \(x = 2\) and \(y=4\)