How many solutions does this linear system have? y = 2x - 5
-8x – 4y = -20
one solution: (-2.5, 0)
one solution: (2.5, 0)
no solution
infinite number of solutions

one solution: (2.5, 0)

Step-by-step explanation:

These are both lines, with different inclines, which by definition, will have one point in common.

So the first two answers are both candidate to be the right answer. To be sure just pick the easiest point and substitute to see if it is the correct point.

You don't even have to check it in both lines, just one will suffice. (To double check if you are right, you could substitute in the other line also).

Check to see if (2.5, 0) is on y = 2x - 5

so substitute x = 2.5 in y = 2x - 5

y = 2 * 2.5 - 5

y = 5 - 5

y = 0

That confirms the right answer.

EXTRA

You don't even have to check it in both lines, just one will suffice. (To double check if you are right, you could substitute in the other line also).

To double check see if (2.5, 0) is on -8x – 4y = -20

substitute x = 2.5 in substitute x = 2.5 in

substitute x = 2.5 and y =0

-8 * 2.5 - 4 * 0 = -20

-20 - 0 = -20

Since -20 = -20 is a true statement that by definition means the point is on the other line also. In other words, it is confirmed once more.