Geometry help? Please

Solve the system of equations
2y = 3x + 8
y = 2x + 3
I don't know what to do with two variables. All I know is you need to equations

When you've got two variables, you need two different equations (which you've got). From there, you need to solve them simultaneously, like so:

2y = 3x + 8 (1)
y = 2x + 3 (2)

Sub (2) into (1)

2(2x + 3) = 3x +8
4x + 6 = 3x + 8
x = 2

Sub x = 2 into (2)

y = 2(2) + 3
= 4 + 3
= 7

Therefore, x = 2 and y = 7

You can check to see if it's right, by subbing x & y, back into both of the equations.

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The method I showed you above is called the substitution method, where you make one of the variables the subject (e.g. y = ..... or x = .....). If they are subject, they must be positive and have no coefficient.

Another way is called the elimination method. This is when you get rid of one of the variables by multiplying a whole equation so that the variables you want to get rid of, have the same coefficient. (e.g. y = 2x + 3 and 2y = 3x + 8.....multiply the first equation by 2, so that the 'y's will both have a coefficient of '2'). After this, you either minus the equations or plus them together-----whichever it is, your aim is to get rid of it, 'eliminate' it.

Anyways, hope this helps! Haha, I think I might've over killed ><

I like to factor using elimination so that's what I'll do here
2y=3x + 8
y = 2x +3
We need to eliminate one of the variables so let's go with Y. Multiply the bottom by -2
2y=3x + 8
-2y = -4x -6
Add the top to the bottom
-x +2
x=2
Plug x into the equations
2y= 14
Divide by 2
y=7
Plug in Y
7= 4 +3
Your answer is (2,7)

2y = 3x + 8 ........................................… [1]
y = 2x + 3 .................................... [2]

From [1] and [2], 2(2x+3) = 3x +8,
4x +6 = 3x +8,
4x -3x = 8 -6,
x = 2 >==================================< ANSWER
FROM [2],
y = 2*2 +3 = 4+3 = 7 >===================< ANSWER