Math homework help? please !?

Question

So, i have this big test tomorrow & i seriously dont know how to do this.
It says ; Solve the system using the method of your choice and tell how many solutions the system has.
1) x + 2y = 5
2x - 2y = 4.
2) x+y=1
X+y=3
How many different solutions does it each have? Please help me

Answer 1

1)x+2y = 5 ------------ (1)

  2x-2y = 4 ------------ (2)

(1)+(2) ⇒x+2y = 5

             2x-2y = 4

          ___________

           3x = 9

Apply division property, divide both sides by 3.

3x/3 =9/3

x = 3

Substitute the x value in (1)

3+2y = 5

2y = 5-3

2y = 2

  y = 1

Solution of first system x = 3 ,y = 1

2)x+y = 1---------- (1)

  x+y = 3 --------- (2)

from (1) and (2) L.H.S are equal then the R.H.S are equal.

1 = 3. this is not possible.

therefore the second system has no solution.