can someone help me on substituting and eliminating systems of equations?! I'm so confused

- Bieber896

can someone help me on substituting and eliminating systems of equations?! I'm so confused

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- schrodinger

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- jim_thompson5910

Post the full problem please

- Bieber896

x=3y-8
5y=19+4x

- Bieber896

@jim_thompson5910

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## More answers

- jim_thompson5910

since x is fully isolated, you can replace the x in the second equation with 3y-8
so `5y=19+4x` turns into `5y=19+4(3y-8)`

- jim_thompson5910

do you see how to solve for y?

- Bieber896

5y=19+12y-32??

- Bieber896

but there's two ys

- jim_thompson5910

get all the y terms to one side
so subtract 12y from both sides to get the y terms to the left side

- Bieber896

-7y=19+(-32)?

- jim_thompson5910

good, then combine like terms on the right side

- Bieber896

-7y=-13

- jim_thompson5910

what comes next

- Bieber896

divide both sides by -7?

- jim_thompson5910

correct

- jim_thompson5910

\[\Large -7y = -13\]
\[\Large \frac{-7y}{-7} = \frac{-13}{-7}\]
\[\Large y = \frac{13}{7}\]
Notice how the two negatives divide to make a positive result

- Bieber896

so y=1.85

- jim_thompson5910

I'd leave it as a fraction because the decimal result is only an approximation

- Bieber896

oh ok

- Bieber896

so then do I plug that in to the next equation?

- jim_thompson5910

yes, you'll plug that into `x=3y-8` to find x

- Bieber896

so x=-2 3/7

- jim_thompson5910

or x = -17/7
so the solution as an ordered pair is \(\LARGE \left( -\frac{17}{7}, \frac{13}{7}\right)\)

- Bieber896

ok thanks so much ! can we just do one more?!

- anonymous

yes

- jim_thompson5910

sure

- Bieber896

y=3x+3
y=2x+1

- jim_thompson5910

y is equal to 3x+3
AND
it's also equal to 2x+1

- jim_thompson5910

since y is equal to those two things, we can set the two equal to each other
basically we're performing a substitution

- jim_thompson5910

y=2x+1
3x+3 = 2x+1 ... replace y with 2x+1
solve for x to get x = ??

- Bieber896

so do I have to get rid of one of the variables?

- anonymous

isolate your x

- jim_thompson5910

move the 2x over
you do this by subtracting 2x from both sides

- anonymous

x=___

- Bieber896

1x+3=+1

- jim_thompson5910

now subtract 3 from both sides to move that 3 to the right side

- Bieber896

1x=-2

- jim_thompson5910

which is the same as x = -2

- Bieber896

yup

- Bieber896

then plug it in

- jim_thompson5910

now plug that into either equation to find y

- Bieber896

so the solution is (-2,3)

- Bieber896

or -3 lol my bad

- jim_thompson5910

yes it's (-2,-3)

- Bieber896

thank you both so much for your help @jim_thompson5910 @tekman1298

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