SAT Desmos Intersections: Solve a Line and Parabola System

Enter these original equations on separate lines:

y = x^2 - 4
y = 2x - 1

Select a curve, then inspect both crossing points. For this system, the intersections are (−1,−3) and (3,5). An x-window from −3 to 5 and y-window from −6 to 10 will show both.

Both y-values must be equal, so x² − 4 = 2x − 1. Rearrange to x² − 2x − 3 = 0, then factor: (x − 3)(x + 1) = 0. Thus x = 3 or −1. Substitution into y = 2x − 1 gives y = 5 or −3. Each pair satisfies the parabola too.

For this system, the sum of the x-values is 2, the larger x-value is 3, and the larger y-value is 5. Those are different possible targets. If a question requires x > 0, only the pair (3,5) meets that restriction.

When an intersection label is rounded, keep enough precision for the task and check the exact equation. For an exact algebraic answer, a decimal graph label may be a starting point rather than the final form. Squaring, canceling or changing denominators can introduce or remove restrictions; substitute candidates into the original equations.

Graph y = x² − 9 and y = x − 3. Equality gives x² − x − 6 = 0, or (x − 3)(x + 2) = 0. The intersections are (3,0) and (−2,−5). Their x-value sum is 1, while their y-value sum is −5. Verify which sum a prompt requests.