Question

How many solutions does the system of equations `-2x + 8y = 6` and `5x + 17= 20y` have?

Answer 1

See a solution process below:

Explanation:

Divide each side of the first equation by `color(red)(-2)` to put the equation in standard form:

`(-2x + 8y)/color(red)(-2) = 6/color(red)(-2)`

`(-2x)/color(red)(-2) + (8y)/color(red)(-2) = -3`

`1x - 4y = -3`

Put the second equation into standard form:

`5x - color(red)(20y) + 17 - color(red)(17) = 20y - color(red)(20y) - color(red)(17)`

`5x - 20y + 0 = 0 - 17`

`5x - 20y = -17`

`(5x - 20y)/color(red)(5) = (-17)/color(red)(5)`

`(5x)/color(red)(5) - (20y)/color(red)(5) = -17/5`

`1x - 4y = -17/5`

The left side of each equation is the same. Therefore, both equations have the same slope. This means both lines are parallel.

However, because the right side of the two equations is different it indicates the two lines are parallel but not the same line.

Therefore, the system of equations has no solution.