Question

Help Please. Will Give Medal. :D
How many solutions does the system have?
x = –4y + 4
2x + 8y = 8 (1 point)
one solution
two solutions
infinitely many solutions
no solution

Answer 1

Solve both equations for y:

Here's the first equation:
x = -4y + 4
4y + x = 4
4y = -x + 4
y = -(1/4)x + 1

Here's the second equation:
2x + 8y = 8
8y = -2x + 8
y = -(2/8)x + 1
y = -(1/4)x + 1

Now that they are both solved for y, they are in the slope-intercept form. This is also called the y = mx + b form.
In y = mx + b, m = slope, and b is the y-intercept. Two lines with the same slope are parallel. They never intersect. If you have a system of linear equation that is represented by two parallel lines, there is no solution.

The slope, m, of the first equation is -(1/4)
The slope, m, of the second equation is -(1/4)
The slopes are equal. You have two possibilities: two parallel lines, or both equations represent the same line.

Now look at the last number in each equation. That is b in y = mx + b. b is the y-intercept, where the lines cross the y-axis. They are both 1. That means it's the same line. That means both lines are really the same line and all points on the line are solutions. Therefore, you have an infinite number of solutions.

Answer 2

You Make It Seem So Easy Thanks.! Can You Hellp With One More?