Solving Linear-Quadratic Systems

Question 1

What are the solutions?

Revolt · Accepted Answer

D: (–3, 4) and (1,0)

Question 2

Question 2

Revolt · Accepted Answer

0

Question 3

David wants to find the solutions of this system of equations: –4x – 7 = yx2 – 2x – 6 = yWhich statement is true?

Revolt · Accepted Answer

B: There is one unique real number solution at (–1, –3).

Question 4

Jordan is solving this system of equations: y = 2x2 + 3 and y – x = 6. Which statements are true about Jordan’s system? Check all that apply.The quadratic equation is in standard form.Using substitution, the system of equations can be rewritten as 2x2 – x – 3 = 0. There are two real number solutions.There are no real number solutions. A solution of the system of equations is (–1, 1.5).

Revolt · Accepted Answer

A: The quadratic equation is in standard form.; B: Using substitution, the system of equations can be rewritten as 2x2 – x – 3 = 0.; C: There are two real number solutions.

Question 5

Which systems of equations have no real number solutions? Check all that apply.y = x2 + 4x + 7 and y = 2 y = x2 – 2 and y = x + 5y = –x2 – 3 and y = 9 + 2xy = –3x – 6 and y = 2x2 – 7x y = x2 and y = 10 – 8x

Revolt · Accepted Answer

A: y = x2 + 4x + 7 and y = 2; C: y = –x2 – 3 and y = 9 + 2x; D: y = –3x – 6 and y = 2x2 – 7x

Question 6

Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and the other is quadratic–without graphing the system of equations.

Revolt · Accepted Answer

Isolate one variable in the system of equations. Use substitution to create a onevariable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.

Question 7

What did you include in your response? Check all that apply.

Revolt · Accepted Answer

A: Use substitution to create a one-variable equation.; B: Set the quadratic equation equal to zero and find the discriminant.; C: The value of the discriminant will tell you how many real number solutions the system of equations has.

Question 8

✔ –2024

Revolt · Accepted Answer

A: ✔ –2

Question 9

–4–2✔ –0.252

Revolt · Accepted Answer

C: ✔ –0.25

Question 10

–4–2–1✔ 2

Revolt · Accepted Answer

D: ✔ 2

Solving Linear-Quadratic Systems Answers

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