Question

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

Answer 1

Post the full problem please

Answer 2

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

Answer 3

@jim_thompson5910

Answer 4

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)`

Answer 5

do you see how to solve for y?

Answer 6

5y=19+12y-32??

Answer 7

but there's two ys

Answer 8

get all the y terms to one side

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

Answer 9

-7y=19+(-32)?

Answer 10

good, then combine like terms on the right side

Answer 11

-7y=-13

Answer 12

what comes next

Answer 13

divide both sides by -7?

Answer 14

correct

Answer 15

\[\Large -7y = -13\]
\[\Large \frac{-7y}{-7} = \frac{-13}{-7}\]
\[\Large y = \frac{13}{7}\]


Notice how the two negatives divide to make a positive result

Answer 16

so y=1.85

Answer 17

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

Answer 18

oh ok

Answer 19

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

Answer 20

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

Answer 21

so x=-2 3/7

Answer 22

or x = -17/7

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

Answer 23

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

Answer 24

yes

Answer 25

sure

Answer 26

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

Answer 27

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

Answer 28

since y is equal to those two things, we can set the two equal to each other

basically we're performing a substitution

Answer 29

y=2x+1

3x+3 = 2x+1 ... replace y with 2x+1

solve for x to get x = ??

Answer 30

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

Answer 31

isolate your x

Answer 32

move the 2x over

you do this by subtracting 2x from both sides

Answer 33

x=___

Answer 34

1x+3=+1

Answer 35

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

Answer 36

1x=-2

Answer 37

which is the same as x = -2

Answer 38

yup

Answer 39

then plug it in

Answer 40

now plug that into either equation to find y

Answer 41

so the solution is (-2,3)

Answer 42

or -3 lol my bad

Answer 43

yes it's (-2,-3)

Answer 44

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