AnswersCA-Common Core Math II A-CRModeling with Quadratic Equations

Solving Linear-Quadratic Systems Answers

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What are the solutions?(–3, 4) and (0,1)(–3, 4) and (–1,0)(3, –4) and (1,0)(–3, 4) and (1,0)

A
(–3, 4) and (0,1)
B
(–3, 4) and (–1,0)
C
(3, –4) and (1,0)
D
(–3, 4) and (1,0)
3

–4–2–1✔ 2

A
–4
B
–2
C
–1
D
2
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✔ –2024

A
–2
B
0
C
2
D
4
84322

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.

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.
D
There are no real number solutions.
E
A solution of the system of equations is (–1, 1.5).
84323

Which systems of equations have no real number solutions? Check all that apply.

A
y = x2 + 4x + 7 and y = 2
B
y = x2 – 2 and y = x + 5
C
y = –x2 – 3 and y = 9 + 2x
D
y = –3x – 6 and y = 2x2 – 7x
E
y = x2 and y = 10 – 8x
84324

What are the solutions?

A
(–3, 4) and (0,1)
B
(–3, 4) and (–1,0)
C
(3, –4) and (1,0)
D
(–3, 4) and (1,0)
84325

✔ –2024

A
–2
B
0
C
2
D
4
84328

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

A
There are no real number solutions.
B
There is one unique real number solution at (–1, –3).
C
There is one unique real number solution at (1, –3).
D
There are two real number solutions at (–1, –3) and (1, –7).
84331

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.

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.

84332

The second solution is ([___], [___]).

Answer not available
84333

–4–2✔ –0.252

A
–4
B
–2
C
–0.25
D
2
84334

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