Question

What is the solution to this system of equations?

X+ 2y = 4
2x-2y = 5
O (3.-53
0
(3.)
no solution
infinitely many solutions

Answer 1

(x, y) = (3, 1/2)

Explanation:

x + 2y = 4

2x - 2y = 5

There is more than one way to do this. I will do it by substitution.

From the first equation, x + 2y = 4, so x = (-2y) + 4

Now, in the second equation, I will replace x with (-2y + 4)

2(-2y + 4) - 2y = 5

-4y + 8 -2y = 5

-6y + 8 = 5

-6y = -3

6y = 3

y = 3/6

---------------------------------> y = 1/2, one part of the answer

Now I can go back to the first equation, and relpace 'y' with 1/2

x + 2(1/2) = 4

x + 1 = 4

-----------------------------------> x = 3, the other part of the answer

So now we believe the solution is (x, y) = (3, 1/2)

Now check the answer, back in the original equations!!

------> In the first equation, we would have 3 + 2(1/2) = 4.

3 + 1 = 4

That is true

-------> In the second equation, we would have 2(3) - 2(1/2) = 5

6 - 1 = 5

That is true

Our answer is found and checked.

(x, y) = (3, 1/2)

Answer 2

X+2y=4

4+2y=x

2(2+y)=x

2x-2y=5

2(x-y)=5

x-y=5/2