Question

Solve the linear system using substitution:

Answer 1

\[-x+\frac{ 2 }{ 9 }y=1\]
\[9x+3y=6\]
I've been trying to solve this for a while now, but can't seem to get the answer, please help!

Answer 2

Multiply each term in the first equation by 9. Then add both of the equations together. This will eliminate the x variable. You can then solve for y.

OR

Solve one of the equations for y. Then substitute the expression for y that you just found into the other equation.

OR

Solve one of the equations for x. Then substitute the expression for x that you just found into the other equation.

AND

View this playlist for examples on how to solve those types of problems.

https://www.youtube.com/playlist?list=PLsX0tNIJwRTwHqLbfCQTZdVUmqz1KBHgv

I hope this helps.

Answer 3

To solve lets change the second equation into slope-intercept form....

First we would subtract by 9x to get it to the other side...

\(\LARGE{(9x-9x)+3y=-9x+6 \rightarrow 3x=-9x+6}\)

Next we would divide by 3 to isolate y....

\(\huge{\frac{3y}{3}=\frac{-9x}{3}+\frac{6}{3}}\)

What would that equal?

Answer 4

\[y=-3+2\]

Answer 5

Your missing the x where the 3 is so it would be...but Correct :)

\(\huge{y=-3x+2}\)

Now we know the equation for y...we can now input y into the first equation...

\(\huge{-x+\frac{2}{9}(-3x+2)=1}\)

In which we would simplify.

Answer 6

oh right, I forgot the x my bad

Answer 7

All's good just make sure to remember next time ;)

Answer 8

So now we solve the equation above...we would first distribute \(\Large{\frac{2}{9}}\) into the equation in parenthesis....

\(\huge{-x+((-3 \times \frac{2}{9})x+(2 \times \frac{2}{9}))=1}\)

What would that equal?

Answer 9

\[-x-\frac{ 6 }{ 9 }x+\frac{ 4 }{ 9 }=1\]

Answer 10

Close but not quite. You need to simplify the fraction...

\(\huge{-x-\frac{2}{3}x+\frac{4}{9}=1}\)

Next combine like terms....

Answer 11

What would..

\(\huge{-x-\frac{2}{3}x=?}\)

Answer 12

\[-\frac{ 5 }{ 3 }x\] ?

Answer 13

Correct :)

\(\huge{-\frac{5}{3}x+\frac{4}{9}=1}\)

Now we need to get the real numbers to one side so we would subtract \(\Large{\frac{4}{9}}\) on both sides...

\(\huge{-\frac{5}{3}x(\frac{4}{9}-\frac{4}{9})=1-\frac{4}{9}}\)

What does that simplify too?

Answer 14

\[-\frac{ 5 }{ 9 }x=\frac{ 5 }{ 9 }\]

Answer 15

Correct :) except the fraction with the variable will stay as `-5/3x`....

Now we would isolate the variable by dividing `-5/3`....

\(\huge{(-\frac{5}{3}\div \frac{5}{3})x=\frac{5}{9} \div \frac{5}{3}}\)

Answer 16

oh ugh im sorry I forgot that too

Answer 17

What do you mean?

Answer 18

I forgot that it was 5/3 and not 5/9

Answer 19

Ooo yea...all's good though :)

Answer 20

anyways
\[x=\frac{ 1 }{ 3 }\] ?

Answer 21

Correct :) Though I forgot to put a negative sign by `5/3` so that was my mistake so....

\(\LARGE{x=-\frac{1}{3}}\)

This is the x-value of the answer now we need to find the y-value...

Now we would input x into the second equation....

\(\huge{y=-3(-\frac{1}{3})+2}\)

Simplify ;)

Answer 22

Were you able to find what y equals?

Answer 23

\[y=3\]

Answer 24

Correct :)

So the solution of the linear system is....\(\LARGE{(-\frac{1}{3},3)}\)

Nicely done!

Answer 25

Ah okay, thank you!

Answer 26

I was really breaking my head over this, thanks a lot :)

Answer 27

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Answer 28

Oh no one had haha, thank you!

Answer 29

:)