What happens to the $y$ terms if you add the two equations together, left side with left side and right side with right side?

After you combine the equations and $y$ disappears, you will have an equation with only $x$. Solve that equation carefully and match your result to one of the answer choices.

In Desmos, type the first equation as 4x - 7y = 8 and the second equation as 3x + 7y = 27. Desmos will graph both lines.

On the graph, locate the point where the two lines intersect. Click or tap on that intersection point to display its coordinates $(x, y)$.

Look at the x-coordinate of the intersection point shown by Desmos; that x-value is the solution to the system and matches one of the answer choices.

Look at the $y$-coefficients in the two equations:

• First equation: $4x - 7y = 8$ (coefficient of $y$ is $-7$)
• Second equation: $3x + 7y = 27$ (coefficient of $y$ is $+7$)

Because these coefficients are opposites, adding the two equations will make the $y$ terms cancel.

Add the left sides and the right sides of the equations:

So the combined equation simplifies to $7x = 35$.

From $7x = 35$, divide both sides by $7$:

So the value of $x$ is $5$, which corresponds to answer choice C.