AnswersMO-Algebra II AMixed Degree Systems

Mixed Degree Systems Answers

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Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola. Equation 1: (x – 3)2 = y – 4 Equation 2: y = -x + bIn order for Tom’s thinking to be correct, which qualifications must be met?

A
b must equal 7 and a second solution to the system must be located at the point (2, 5).
B
b must equal 1 and a second solution to the system must be located at the point (4, 5).
C
b must equal 7 and a second solution to the system must be located at the point (1, 8).
D
b must equal 1 and a second solution to the system must be located at the point (3, 4).
2
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What are the solutions of the following system?

Question illustration
A
and
Option A
B
and
Option B
C
(6, 312) and (–6, 312)
D
(6, 312) and (–6, –264)
3

Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest number of possible solutions to this system?

A
0
B
1
C
2
D
4
4

What are the solutions of the following system?

Question illustration
A
(0, –5) and (–5, 5)
B
(0, –5) and (5, –15)
C
(0, –5) and (–4, 3)
D
(0, –5) and (4, –13)
5

Consider the following system of equations.Which statement describes why the system has infinite solutions?

Question illustration
A
The equations represent parabolas that result in graphs that do not intersect.
B
The equations represent circles that result in graphs that do not intersect.
C
The equations represent parabolas that result in the same graph.
D
The equations represent circles that result in the same graph.
6

The vertex of a parabola is in the first quadrant of a coordinate grid. A line with a negative slope passes through the origin. If the parabola and line intersect at the origin, which statement must be true?

A
The parabola opens downward.
B
The parabola opens upward.
C
The slope of the line is equal to –1.
D
The slope of the line is not equal to –1.
7

Which equation is part of solving the system by substitution?

Question illustration
A
4(y + 11)2 – 3y2 = 8
B
4(11 – y)2 – 3y2 = 8
C
4(y – 11)2 – 3y2 = 8
D
4(–11y)2 – 3y2 = 8
8

Which graph shows the system ?

Question illustration
A
On a coordinate plane, a graph of a circle and a parabola are shown. The circle has a center at (0, 0) and a radius of 3 units. The parabola opens down and intersects the circle at (negative 2, negative 2), has a vertex at (0, 2), and intersect the circle again at (2, negative 2).
Option A
B
On a coordinate plane, a graph of a circle and a parabola are shown. The circle has a center at (0, 0) and a radius of 3 units. The parabola opens up and intersects the circle at (negative 2, 2), has a vertex at (0, negative 2), and intersect the circle again at (2, 2).
Option B
C
On a coordinate plane, a graph of a circle and a parabola are shown. The circle has a center at (0, 3) and has a radius of 3 units. The parabola opens up and intersects the circle at (negative 2, 5), has a vertex at (0, 2), and intersects the circle again at (2, 5).
Option C
D
On a coordinate plane, a graph of a circle and a parabola are shown. The circle has a center at (0, 3) and has a radius of 3 units. The parabola opens down and goes through (negative 2, negative 2), has a vertex at (0, 2), and goes through (2, negative 2).
Option D
9

Which graph represents the solution of the system ?

Question illustration
A
On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 4 units. The line has a negative slope and goes through (negative 3, 4), (0, 1), and (1, 0).
Option A
B
On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 2 units. The line has a positive slope and goes through (negative 3, negative 4), (0, negative 1), and (1, 0).
Option B
C
On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 4 units. The line has a positive slope and goes through (negative 3, negative 4), (0, negative 1), and (1, 0).
Option C
D
On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 2 units. The line has a negative slope and goes through (negative 3, 4), (0, 1), and (1, 0).
Option D
10

What are the solutions to the following system?

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

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