Modeling with Systems Answers
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What are the solutions of the following system?
A
and
B
and
C
(6, 312) and (–6, 312)D
(6, 312) and (–6, –264)3
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.4
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.
5
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.
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