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Solving Systems by Graphing questions quiz. Let's take this quiz and learn more about it!
Questions and Answers
1.
Solve by graphing.y = -2x - 3y = 3x + 2
Explanation The given answer (-1,-1),(-1, -1) represents the coordinates of two points that satisfy both equations y = -2x - 3 and y = 3x + 2. These points are (-1, -1) and (-1, -1), which means that when x is -1, y is also -1 for both equations. Therefore, these points satisfy both equations simultaneously and are the solution to the system of equations.
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2.
Solve by graphing.y = -2x + 4y = x - 5
Explanation The given answer (3,-2),(3, -2) is correct. It represents the solution to the system of equations y = -2x + 4 and y = x - 5. When graphed, these two equations intersect at the point (3,-2), which means that the coordinates (3,-2) satisfy both equations simultaneously. Therefore, (3,-2) is the solution to the system of equations.
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3.
Solve by graphing.y = -3x + 1y = -x + 5
Explanation The given answer (-2,7),(-2, 7) is correct because it represents the coordinates of the point where the two lines intersect. By graphing the equations y = -3x + 1 and y = -x + 5, we can see that they intersect at the point (-2,7). The repetition of the point (-2,7) in the answer is likely a typographical error.
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4.
Solve by graphing.y = -x + 5y = x - 3
Explanation The given answer (4,1),(4, 1) is correct. It represents the coordinates of the point where the two equations intersect on the graph. By substituting the x-coordinate (4) into both equations, we find that y is equal to 1 in both cases. Therefore, the point (4,1) satisfies both equations and is the solution to the system of equations.
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5.
Solve by graphing.5y + 5x = 103y + 6x = -9
Explanation The correct answer is (-5,7), (-5,7). This means that the solution to the system of equations is x = -5 and y = 7. By substituting these values into the original equations, we can verify that they satisfy both equations. Therefore, (-5,7) is the correct solution.
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6.
Solve by graphing.4y + 4x = 48y + 16x = 40
7.
2y + 8x = 46y - 6x = -18
Explanation The given system of equations is 2y + 8x = 4 and 6y - 6x = -18. The answer (1,-2),(1,-2) means that the solution to both equations is x = 1 and y = -2. This can be verified by substituting these values into both equations and confirming that they satisfy the equations.
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8.
Solve by graphing.10y - 40x = 1107y + 14x = -7
Explanation The given answer is (-2,3),(-2, 3). This means that the coordinates of the point of intersection of the two equations are (-2,3). The two equations are 10y - 40x = 110 and 7y + 14x = -7. By graphing these equations, we can find the point where the two lines intersect. The fact that the answer is given twice with the same coordinates suggests that there is only one point of intersection, which is (-2,3).
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