Mixed Degree Systems Answers

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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)
2
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Which system is equivalent to ?

Question illustration
A
StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 2 2nd row x = y minus 2 EndLayout
Option A
B
StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 2 2nd row x = y + 2 EndLayout
Option B
C
StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 8 y minus 8 2nd row x = y + 2 EndLayout
Option C
D
StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 8 y minus 8 2nd row x = y minus 2 EndLayout
Option D
3

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.
Option A
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.
Option B
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.
Option C
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.
Option D
4

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
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

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

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 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
9

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)
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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