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2.3 Systems Involving Nonlinear Equations - Line + parabola intersections
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The figure presents the graph of a curve and a line in the x y plane, with the origin labeled O. The numbers negative 10 through 10, in increments of 5, are indied on each axis. The line begins slightly below the x axis and to the left of the y axis, crosses the x axis at negative 10 and crosses the y axis at approximately 2. It ends above the x axis and to the right of the y axis. The curve is in the shape of a parabola that opens upward and has its vertex at approximately negative 2 point 5 on the y axis. The parabola crosses the x axis at approximately negative 5 and 5. The line and curve intersect at the point with approximate coordinates negative 6 comma 1, and at the point with approximate coordinates 7 comma 4.

A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the xy-plane above. How many solutions does this system have?

A.

0

B.

1

C.

2

D.

3

A system of equations consists of a quadratic equation and a linear equation. The equations in

Hard-difficulty · SAT Math · Systems Involving Nonlinear Equations — Line + parabola intersections. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice C is correct. The solutions to a system of two equations correspond to points where the graphs of the equations intersect. The given graphs intersect at 2 points; therefore, the system has 2 solutions.

Choice A is incorrect because the graphs intersect. Choice B is incorrect because the graphs intersect more than once. Choice D is incorrect. It’s not possible for the graph of a quadratic equation and the graph of a linear equation to intersect more than twice.

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