Sylvie finds the solution to the system of equations by graphing. y = x + 1 and y = x – 1 Which graph shows the solution to Sylvie’s system of equations?

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Graphs of y = x+- 1 and of y = x - 1 are shown in the figure below. The intersection of the two graphs is the solution for the two equations. Answer: There is no solution. Explanation: It is clear that the two lines are parallel and will never intersect. Note that the equation for a straight line is of the form y = mx + b where m = slope, b = y-intercept. y = x + 1 has slope of m=1. y = x - 1 has slope of m=1. The two slopes are equal. Because parallel lines do not intercept, there is no solution.

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