Once you have $y$ written in terms of $x$, substitute that expression into the other equation $x^2 - y = 7$ so that the new equation has only $x$ in it.

After you solve the resulting equation for $x$, use $x + y = 5$ to find the corresponding $y$-values. Then see which of the answer choices match the $(x, y)$ pair(s) you found.

For each answer choice, plug $x$ and $y$ into both equations and check whether both are true. Only one ordered pair will make both equations true at the same time.

Rewrite each equation in the form $y = \text{expression}$:

• From $x + y = 5$, get $y = 5 - x$.
• From $x^2 - y = 7$, get $y = x^2 - 7$. In Desmos, enter y = 5 - x and y = x^2 - 7 as two separate graphs.

Look at the point(s) where the line and the parabola intersect. Hover or tap on each intersection to see its coordinates, then choose the answer option whose ordered pair exactly matches one of those intersection points.

From the first equation,

solve for $y$:

Now you can replace $y$ in the second equation with $5 - x$.

Substitute $y = 5 - x$ into the second equation $x^2 - y = 7$:

Distribute the minus sign:

Move all terms to one side:

Now solve this quadratic.

Factor the quadratic:

So the possible $x$-values are

Use $y = 5 - x$ to find each corresponding $y$:

• If $x = -4$, then $y = 5 - (-4) = 9$.
• If $x = 3$, then $y = 5 - 3 = 2$.

So the system has two solutions: $(-4, 9)$ and $(3, 2)$.

Compare the solution pairs $(-4, 9)$ and $(3, 2)$ to the answer options:

• (2, 3)
• (-4, 2)
• (4, 1)
• (3, 2)

Only $(3, 2)$ appears in the list, so the ordered pair that satisfies the system is $(3, 2)$.