Question

How many soultions does this linear system have? y=2x-5 -8x-4y=-20 ?

Answer 1

One solution, since the lines intersect at only one point.

Explanation:

These two equations should be separated by a comma or written on two separate lines. I'm assuming that you meant:

y=2x-5

-8x-4y=-20

First, we need to ensure that both of these equations are written in the same format, y = mx + b. The first equation is already in that format: y = 2x - 5. The first step in rewriting the second equation is to add 8x to both sides:

+ 8x -8x -4y = 8x = -20, or -4y = 8x - 20.

Next, we divide all three terms by -4 to isolate y:

y = -2x + 5

Then the given system is equivalent to

y = 2x - 5

y = -2x + 5

We could either solve this system or analyze it without solving it:

Because these two equations have different slopes, their graphs are not parallel. This indicates that the lines intersect at only one point.

Answer 2

One solution.

Explanation:

I'm assuming you're allowed to use your graphing calculator for this problem. So, if you plug in the two lines in a graphing calculator, you'd see they have one solution.

If you don't have access to a calculator, though, you can find out the number of solutions by changing the second one to y=mx+b.

This is done like so:

-8x-4y=-20

-8x-4y+20=0

-8x+20=4y

y=-2x+20

You can see that they are not the same equation, so it would have one solution because they would cross once.