# Thread: Solving equations by substition help

1. ## Solving equations by substition help

Here is the problem:

solve these equations using substiution:
2x+4y=8
3x+2y+0

I figured Y for the 2nd one first so I got
2y=0+3x which equals y=3/2x

substitute that into the first one

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

2x+6x=8
x=1

put that into y=3/2x which I got 3/2 for Y

then I went to check and only one worked, where am I going wrong? Thanks in advance!

2. Hello, MathMack!

A simple error . . .

Solve by substiution: . $\begin{array}{ccc}2x+4y &=&8 \\3x+2y&=&0 \end{array}$

I found y for the 2nd one and got: . $y \:=\:\frac{3}{2}x$

It should have been: . $y \:=\:{\bf{\color{red}-}}\frac{3}{2}x$

3. how did you get negative if you don't mind, and thanks for the help

4. nevermind i got it! i'll work it out and see what happens

5. when i go to check i get -8 for the 1st equation?

6. nevermind, lol, forgot a negative, works out great I have another one i'm having trouble with, if you don't mind

7. this one is by elimination

3x+4y=2
2x-3y= -10

Where do I start?

8. Originally Posted by MathMack
Here is the problem:

solve these equations using substiution:
2x+4y=8
3x+2y+0

I figured Y for the 2nd one first so I got
2y=0+3x which equals y=3/2x

substitute that into the first one

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

2x+6x=8
x=1

put that into y=3/2x which I got 3/2 for Y

then I went to check and only one worked, where am I going wrong? Thanks in advance!
2x + 4y = 8
2x = 8 - 4y
x = 4 - 2y

Substitute into the other equation:

3(4 - 2y) + 2y = 0
12 - 6y + 2y = 0
12 - 4y = 0
12 = 4y
y = 3

And go back to the other equation:

2x + 4(3) = 8
2x + 12 = 8
2x = -4
x = -2

this one is by elimination

3x+4y=2
2x-3y= -10

Where do I start?
You want to start by making the coefficients in front of one of the variables the same by multiplying each equation by a constant. I am going to make the coefficients of x equivalent.

2(3x + 4y = 2) => 6x + 8y = 4
3(2x - 3y = -10) => 6x - 9y = -30

Now, subtract these two equations.

(6x + 8y = 4)
- (6x - 9y = -30) [Remember that subtracting a negative is equivalent to addition]
--------------------
0x + 17y = 34
17y = 34
y = 2

Now, just like in substitution, use one of the original equations to solve for x.

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

Good luck. :>

9. Thanks figured it all out, Thanks again!

10. I have another one for you if you can help me please, the teacher says use whatever method I chose and the question is

x+4y=9
2x+y=4

Don't know where to start. Thanks

11. Nervmind, I figured it out!