SOLUTION: How do i solve the system 3x+2y=4 and y-2x=9

Question 837506: How do i solve the system 3x+2y=4 and y-2x=9
Found 2 solutions by richard1234, josh_jordan:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
y-2x = 9 <--> y = 2x+9 from second eq.

Substitute this expression for y into the first equation and solve for x. Then solve for y.
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
The easiest way to solve this system of linear equations is by substitution, since one of the variables has no number in front of it. Since the second equation contains a letter without a number in front of it, we will isolate that letter on one side of the equal sign, so y - 2x = 9 will become:

y = 9 + 2x

Next, we will replace y in the first equation, with 9 + 2x:

3x + 2(9 + 2x) = 4

Now, multiply 2 by everything inside the parenthesis, which will give us the following equation:

3x + 18 + 4x = 4

Combine 3x and 4x, which gives us:

7x + 18 = 4

Subtract 18 from both sides of the equal sign, giving us:

7x = -14

Divide both sides of the equal sign by 7, in order to get x by itself. This gives us:

x = -2

Now that we have the value of x, we can replace x with -2 in our rewritten second equation: y = 9 + 2x will become:

y = 9 + 2(-2), which gives us:

y = 9 - 4, which leaves us with

y = 5

Therefore, x = -2 and y = 5
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