AnswersIntegrated Math 2A - Mr. Katykhin 26Solving Linear-Quadratic Systems

Solving Linear-Quadratic Systems Answers

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The first step in determining the solution to the system of equations, y = –x2 – 4x – 3 and y = 2x + 5, algebraically is to set the two equations equal as –x2 – 4x – 3 = 2x + 5. What is the next step?

A
Set y = 0 in y = –x2 – 4x – 3.
B
Factor each side of the equation.
C
Use substitution to create a one-variable equation.
D
Combine like terms onto one side of the equation.
2
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Which graph most likely shows a system of equations with one solution?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

Which line will have no solution with the parabola y – x + 2 = x2?

Question illustration
A
y = –3x –3
B
y = –2x –3
C
y = 2x –3
D
y = 3x –3
4

Which represents the solution(s) of the system of equations, y = x2 – 4x – 21 and y = –5x – 22? Determine the solution set algebraically.

A
(–1, –17)
B
(1, –27)
C
(–1, –17) and (1, –27)
D
no solutions
5

Which graph shows a system of equations with a solution at (–1, 1)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

Which graph most likely shows a system of equations with two solutions?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

The first two steps in determining the solution set of the system of equations, y = x2 – 2x – 3 and y = –x +3, algebraically are shown in the table. Which represents the solution(s) of this system of equations?

Question illustration
A
(3, 0) and (–2, 5)
B
(–6, 9) and (1, 2)
C
(–3, 6) and (2, 1)
D
(6, –3) and (–1, 4)
9

Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?

Question illustration
A
(1, 0) and (0, –1)
B
(–2, –3) and (1, 0)
C
(0, –3) and (1, 0)
D
(–3, –2) and (0, 1)
10

Question text not available

Question illustration
A
-1
B
-3
C
0
D
3
11

The first three steps in determining the solution set of the system of equations algebraically are shown.y = x2 − x − 3 y = −3x + 5

Question illustration
A
(−2, −1) and (4, 17)
B
(−2, 11) and (4, −7)
C
(2, −1) and (−4, 17)
D
(2, 11) and (−4, −7)
12

Which represents the solution(s) of the graphed system of equations, y = x2 + x – 2 and y = 2x – 2?

Question illustration
A
(–2, 0) and (0, 1)
B
(0, –2) and (1, 0)
C
(–2, 0) and (1, 0)
D
(0, –2) and (0, 1)
13

Which graph most likely shows a system of equations with no solutions?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.

A
(–2, 0)
B
(–2, 0) and (2, 0)
C
(–2, 0) and (3, 5)
D
no solutions
15

The first two steps in determining the solution set of the system of equations, y = x2 – 6x + 12 and y = 2x – 4, algebraically are shown in the table. Which represents the solution(s) of this system of equations?

Question illustration
A
(4, 4)
B
(–4, –12)
C
(4, 4) and (–4, 12)
D
(–4, 4) and (4, 12)
16

Which parabola will have one real solution with the line y = x – 5?

Question illustration
A
y = x2 + x – 4
B
y = x2 + 2x – 1
C
y = x2 + 6x + 9
D
y = x2 + 7x + 4

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