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.
--7y = x + 34 2x + 6y = -36
A) infinite number of solutions
B) no solution
C) one solution

Question

Quizplus · Accepted Answer

To determine the number of solutions, we first express both equations in slope-intercept form (y = mx + b). For the first equation, -7y = x + 34, we divide by -7 to get y = -1/7x - 34/7. For the second equation, 2x + 6y = -36, we rearrange it to get 6y = -2x - 36 and then divide by 6 to get y = -1/3x - 6. Since the slopes (-1/7 and -1/3) are different, the lines will intersect at exactly one point, indicating one solution.

Express Each Equation in Slope-Intercept Form