Solving Linear Systems Graphically Answers
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Analyze the solution set of the following system by following the given steps. 2x + y = 5 3y = 9 − 6x Write each equation in slope-intercept form. y = x + y = x +
Solve the system. 2x + y = −3 −2y = 6 + 4x Write each equation in slope-intercept form. y = x + y = x +
intersect at one point✔ coincideare parallel
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Consider the system:y = 3x + 5y = ax + bWhat values for a and b make the system inconsistent? What values for a and b make the system consistent and dependent? Explain.
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Solve the system. 2x + y = 3 −2y = 14 − 6x Write each equation in slope-intercept form. y = x + y = x + How do the slopes and y–intercepts of the two equations compare?
Explain how you can determine that the following system has one unique solution – without actually solving the system.
Write each equation in slope-intercept form. Find that the slope of the first line is –2. Find that the slope of the second line is –1. Since the slopes of the lines are different, the lines must have a point of intersection. The point of intersection is the unique solution.
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How should you modify the graph to show the solution to the system of inequalities below? Check all that apply.
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-3
no solution.exactly one solution.✔ infinitely many solutions.
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3
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-2
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-2
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3
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-3
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-7
What do the equations have in common? How are they different?
The equations have the same slope, -2, but they have different y-intercepts. The y-intercepts are 4 and -2.
What do the equations have in common?
The slopes are the same. The y-intercepts are the same. The lines are the same.
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The slopes are different and the y-intercepts are different.
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intersect at one pointcoincide✔ are parallel
✔ intersect at one pointcoincideare parallel
✔ no solution.exactly one solution.infinitely many solutions.
no solution✔ exactly one solutioninfinitely many solutions
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