Question

X+y=5

3x-y=-5
is it no solutions, all solutions, or one solution?
please show your work.

Answer 1

There's one solution

(0,5)

Explanation:

There's one solution

We can tell this is true because of the 3x in the second on and just hte x in the first. If you look closely you'll see the coefficents for the x values is the only difference between the two.

Let's now solve

We need to get a positive variable by itself

let's take x+y=5 and solve for y

x-5= -y

y= -x+5

We can then plug this y value into the other equation

3x-(-x+5)= -5

3x+x-5= -5

4x= 0

x=0

Let's then plug this value in for x into any of the beginning equations

0+y=5

y=5

Answer 2

One solution

Explanation:

x+y=5

3x-y=-5

Add the equations together will get you:

4x=0

Divide the 0 by 4 to get the x alone will get you

x=0