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Back to Exercise: Solve linear-quadratic systems

Exercises: Solve Linear-Quadratic Systems

Show all algebraic steps. For each solution (x, y), verify in both original equations.

Grade 10·17 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-c-7
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A

Recall / Warm-Up

Three side-by-side diagrams showing a line and parabola with 2 intersections, 1 tangent point, and 0 intersections.
1.

The diagram below shows three cases for a line intersecting a parabola. How many intersection points does a line and a parabola have in the tangent case?

2.

After substituting the linear equation into the quadratic in a linear-quadratic system, you get the equation x2−5x+6=0x^2 - 5x + 6 = 0. How many real solutions does this system have?

3.

The equation x2+y2=9x^2 + y^2 = 9 represents which geometric shape?

B

Fluency Practice

Coordinate plane showing the line y = x + 2 and parabola y = x squared with labeled intersection points at (2,4) and (-1,1).
1.

Solve the system y=x+2y = x + 2 and y=x2y = x^2 algebraically. Show all steps and verify both solutions in both original equations.

2.

Solve the system y=4x−4y = 4x - 4 and y=x2y = x^2 algebraically. After substituting, compute the discriminant before solving to predict the number of solutions.

3.

Solve the system y=−3xy = -3x and x2+y2=3x^2 + y^2 = 3 algebraically. This is the CCSS example for this standard. Give exact coordinates.

4.

Solve the system y=x+1y = x + 1 and y=x2−3x+5y = x^2 - 3x + 5 algebraically. Rearrange to standard form before choosing a solving method.

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