AnswersCrowley Summer 26 Credit Recovery Algebra 2 ASolving Systems of Equations in Three Variables

Modeling with Systems Answers

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1
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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
2
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How many solutions exist for the system of equations in the graph?

Question illustration
A
one
B
two
C
three
D
four
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

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
5

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.
6

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).
7

How many solutions exist for the mixed-degree system graphed below?

Question illustration
A
zero
B
one
C
two
D
three
8

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

Question illustration
A
Each graph has one y-intercept, which is a solution.
B
Each graph has one vertex, which is a solution.
C
The graphs of the equations intersect the x-axis at two places.
D
The graphs of the equations intersect each other at two places.
9

How many solutions exist for the mixed-degree system graphed below?

Question illustration
A
zero
B
one
C
two
D
three
10

The center of a circle is at the origin on a coordinate grid. The vertex of a parabola that opens upward is at (0, 9). If the circle intersects the parabola at the parabola’s vertex, which statement must be true?

A
The maximum number of solutions is one.
B
The maximum number of solutions is three.
C
The circle has a radius equal to 3.
D
The circle has a radius less than 9.

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