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

Given equations

1) x + 2y = 5 -------->  (Equation 1)

   2x - 2y = 4  -------->  (Equation 2)

Substitution method:

Add the equation 1 and 2.

3x = 9

Divide each side by 3.

3x/3 = 9/3

x = 3

There fore x = 3.

Substitute x = 3 in x + 2y = 5.

3 + 2y = 5

Subtract 3 from each side.

2y = 5 - 3

2y = 2

Divide each side by 2.

2y/2 = 2/2

y = 1

The solution point of (x, y) = (3, 1).

Check:

To check the solution, substitute (3, 1) in x + 2y = 5.

3 + 2(1) = 5

3 + 2 = 5

5 = 5

The solution is true.

Second method is Graphing method:

Comments

Therefore, the system has exactly one solution.

The solution point is (3, 1).

Answer 2

2)x+y=1________(1)

  x+y=3_________(2)

multiple (1) with 3 and (3) with 1

  3x+3y=3

   x+y=3

______________

(1) _ (2)⇒2x+2y=0

divide each sides with 2

x+y=0

x=-y

here is no solution.

graphing method

 

Comments

Given two lines are parallel lines.

So, there is no solution exists.