Question 101732
There are three ways to solve systems of equations with two variables.
They are 
1. Substitution Method
2. Elimination Method 
3. Graphing

For this problem I will demonstrate the substitution method.
Ok so we are working with two equations:
y = 2x + 5
3x - y = 4

The first equation shows that 2x+5 equals y So we are going to take 2x+5 and substitute it for y in the second equation. So you can see that is why this is called the substitution method.
ok we have 
3x - y = 4
now substitute y with 2x+5
3x - (2x + 5) = 4
now we can solve for x
first distribute the negative sign across (2x + 5)
3x - 2x - 5 = 4
next combine like terms
x - 5 = 4
now solve for x by adding 5 to both sides
x = 9
<b>ok we found our first variable x = 9</b>
now use this value for x and substitute it in the first equation. 
and solve for y

y = 2x + 5
y = 2(9) + 5
y = 18 + 5
y = 23
<b>now we have found the second variable y = 23</b>
All that is left to do is check our answers.
y = 2x + 5
23 = 2(9) + 5
23 = 18 + 5
23 = 23
now check the answers in the second equation
3x - y = 4
3(9) - 23 = 4
27 - 23 = 4
4 = 4
So the answers we got work for both equations.
Thats it.