Sylvie solved this system of equations. y = 5x + 2, y = 8 – x 8 – x = 5x + 2 8 = 6x + 2 6 = 6x x = 1 8 – 1 = 5(1) + 2 7 = 7 There are infinite solutions to this system. Sylvie solved this system of equations. y = 5x + 2, y = 8 – x 8 – x = 5x + 2 8 = 6x + 2 6 = 6x x = 1 8 – 1 = 5(1) + 2 7 = 7 There are infinite solutions to this system. When Sylvie verified the solution on a graph, the lines intersected at one point. What was her error? She forgot to put both equations in slope-intercept form. She made an arithmetic mistake in the last step. She found the incorrect value of x. She did not substitute the value of x into one of the original equations to find y.
// Solve equation [1] for the variable y [1] y = 5x // Plug this in for variable y in equation [2] [2] -2•(5x) + 6x = 12 [2] - 4x = 12 // Solve equation [2] for the variable x [2] 4x = - 12 [2] x = - 3 // By now we know this much : y = 5x x = -3 // Use the x value to solve for y y = 5(-3) = -15 Solution : {y,x} = {-15,-3}
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