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.
-2x + y = 8 8x + 4y = 32
A) one solution
B) no solution
C) infinite number of solutions

Question

Quizplus · Accepted Answer

To write the equations in slope-intercept form, we need to solve for y in each equation:

2x + y = 8
y = -2x + 8

8x + 4y = 32
4y = -8x + 32
y = -2x + 8

As we can see, the two equations have the exact same slope-intercept form, meaning they represent the same line. Therefore, there are an infinite number of solutions to this system of equations. First, we need to express both equations in slope-intercept form, which means solving for y:
2x + y = 8 
y = -2x + 8

8x + 4y = 32 
4y = -8x + 32 
y = -2x + 8

As we can see, both equations have the same slope (-2) and y-intercept (8), which means they represent the same line. Therefore, there are infinitely many solutions to this system of equations, and the answer is C.

Express Each Equation in Slope-Intercept Form