Mixed Degree Systems Answers
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1
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Which graph shows a system of equations with no solutions?
A
On a coordinate plane, the graphs of 2 circles are shown. Both circles have a center at (0, 0). The smaller circle is within the larger circle and the smaller circle has a radius that is 2 units smaller than the larger circle.
B
On a coordinate plane, a graph of a line and a parabola are shown. The line is horizontal to the x-axis at y = negative 5. The parabola opens up and its vertex on the line.
C
On a coordinate plane, the graphs of 2 circles are shown. Both circles are in quadrant 1, and they intersect each other.
D
On a coordinate plane, the graphs of 2 parabolas are shown. Both parabolas open up and they intersect each other at (0, 0). The first parabola has a vertex in quadrant 3 and the second parabola has a vertex in quadrant 4.
2
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Which graph shows a system of equations with exactly one solution?
A
On a coordinate plane, a graph shows a smaller circle within a larger circle in quadrants 2 and 3. The larger circle is in both quadrants, but the smaller circle is in the middle of the larger circle in quadrant 2.
B
On a coordinate plane, the graph of a circle and a parabola are shown. The circle is in quadrant 3. The parabola has a vertex in quadrant 1 and goes through the circle in quadrant 3.
C
On a coordinate plane, the graph of a circle and a straight line are shown. The circle is in quadrant 1. The line has a negative slope and starts in quadrant 2, crosses the y-axis at (0, 3), and crossed the x-axis at (3, 0). The line does not go through the circle.
D
On a coordinate plane, the graphs of 2 parabolas are shown. One parabola opens down and the other opens up. They share the same vertex in quadrant 2.
3
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).4
Consider the following system of equations.Which statement describes why the system has two solutions?
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.6
What are the solutions of the following system?
A
(0, –5) and (–5, 5)B
(0, –5) and (5, –15)C
(0, –5) and (–4, 3)D
(0, –5) and (4, –13)7
Which graph shows the system ?
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).
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).
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).
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).
8
How many solutions exist for the system of equations in the graph?
A
oneB
twoC
threeD
four9
Parabola A can be represented using the equation (x + 3)2 = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A. Which best describes the reasonableness of her claim?
A
Isabel is correct because the y-intercept of line B is (0, 9) and the value of y when x = 0 in parabola A is 9.B
Isabel is correct because the y-intercept of line B is (9, 0) and the value of x when y = 0 in parabola A is 9.C
Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.D
Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the x-intercept of the equations, not the vertex.10
Which graph represents the solution of the system ?
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).
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).
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).
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).
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