Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-5x - 7y = -9 5x - 7y = 9
A) infinite number of solutions
B) one solution
C) no solution

Question

Quizplus · Accepted Answer

By rearranging the equations in slope-intercept form:
5x - 7y = -9 becomes y = (5/7)x + 9/7
5x - 7y = 9 becomes y = (5/7)x - 9/7
These equations have different y-intercepts, which means they have different lines. Therefore, the system of equations has no solution. First, let's rewrite each equation in slope-intercept form.

5x - 7y = -9  becomes y = (5/7)x + 9/7

5x - 7y = 9  becomes y = (5/7)x - 9/7

Notice that the slopes of the two equations are the same (5/7). This means that the two lines are parallel and will never intersect. Therefore, there are no solutions to the system of equations.

So the best choice is C, no solution.

Express Each Equation in Slope-Intercept Form