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

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

Mathematics
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Post the full problem please
x=3y-8 5y=19+4x

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Other answers:

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)`
do you see how to solve for y?
5y=19+12y-32??
but there's two ys
get all the y terms to one side so subtract 12y from both sides to get the y terms to the left side
-7y=19+(-32)?
good, then combine like terms on the right side
-7y=-13
what comes next
divide both sides by -7?
correct
\[\Large -7y = -13\] \[\Large \frac{-7y}{-7} = \frac{-13}{-7}\] \[\Large y = \frac{13}{7}\] Notice how the two negatives divide to make a positive result
so y=1.85
I'd leave it as a fraction because the decimal result is only an approximation
oh ok
so then do I plug that in to the next equation?
yes, you'll plug that into `x=3y-8` to find x
so x=-2 3/7
or x = -17/7 so the solution as an ordered pair is \(\LARGE \left( -\frac{17}{7}, \frac{13}{7}\right)\)
ok thanks so much ! can we just do one more?!
yes
sure
y=3x+3 y=2x+1
y is equal to 3x+3 AND it's also equal to 2x+1
since y is equal to those two things, we can set the two equal to each other basically we're performing a substitution
y=2x+1 3x+3 = 2x+1 ... replace y with 2x+1 solve for x to get x = ??
so do I have to get rid of one of the variables?
isolate your x
move the 2x over you do this by subtracting 2x from both sides
x=___
1x+3=+1
now subtract 3 from both sides to move that 3 to the right side
1x=-2
which is the same as x = -2
yup
then plug it in
now plug that into either equation to find y
so the solution is (-2,3)
or -3 lol my bad
yes it's (-2,-3)
thank you both so much for your help @jim_thompson5910 @tekman1298

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