Solving Linear Systems Graphically Answers
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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.
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✔ no solution.exactly one solution.infinitely many solutions.
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.
no solution.exactly one solution.✔ infinitely many solutions.
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