Question

Use substitution to solve the system of equations. Enter your answer as an ordered pair; example: (4, -5)

{2x - y = 2
3x - 2y = 11

Answer 1

If you must use substitution, choose whichever of the 2 given equations can be more easily solved for either x or y. Then, substitute your result into the other equation and solve for the remaining variable. Show your work.

Answer 2

still needs help mate?

Answer 3

yes i do

Answer 4

2x - y = 2
3x - 2y = 11
That's the system of equations you have
you have to use substitution method
correct? don't answer that we know already
so anyway one of those equations MUST have only one variable on one side
the easiest is to isolate y for the 1st equation
let's see
2x - y = 2
isolate y
-y = 2 - 2x
y = -2 + 2x

so now mate we have
y = -2 + 2x
3x - 2y = 11

now we will SUBSTITUTE y value in the 2nd equation
3x -2(-2 + 2x) = 11
Now solve this for x

Answer 5

Even if your first efforts are wrong, you'd learn more by trying to solve this problem than by doing nothing.

Hint: 2x - y = 2 is easier to solve for y than is the other equation. So, solve 2x - y = 2 for y. You'll get a 2-term expression in x. Substitute this expression for y in the other equation.

Will.H has explained this well, already. Please share your work now.

Answer 6

let me know if you need additional help

Answer 7

Cam: When you have others helping you, it's most polite to respond right away.

Answer 8

right right sorry im still working this out the math

Answer 9

okay so so far ive got - 14 and -16

Answer 10

see @mathmale is a really wonderful professor

Answer 11

he'll take it from here
have to help others

Answer 12

Cam: Easier for the rest of us to help you meaningfully if you show how you got your results.

Thanks, Will, for the lovely compliment.

Answer 13

my pleasure

Answer 14

If you haven't already, solve 2x - y = 2 for y. Hint: This might be easier if you change the signs of all 3 terms.

Answer 15

well wouldnt that be y = -2 + 2x

Answer 16

Yes, very good. Now, look at the second equation:

Answer 17

3x - 2y = 11

Enclose the "y" in parentheses: 3x - 2( y )= 11

Now throw out "y" and replace it with your "-2+2x."

Answer 18

3x - 2 (y = -2 + 2x) = 11

Answer 19

Yes, but OMIT the "y=" part completely. Your result?

Answer 20

y is GONE. So is the extra "=" sign.

Answer 21

3x - 2 (-2 + 2x) = 11

Answer 22

You're fast, and that's correct. Please multiply out 12(-2+2x) now. What is the simplified form of your 3x - 2 (-2 + 2x) = 11 ?

Answer 23

I'm sorry, that's "multiply out 2(-2+2x)."

Answer 24

You should get something like this: 3x + ? - ? = 11.

Answer 25

im lost now.. multiply out?

Answer 26

-2(-2+2x) implies MULTIPLICATION.

Answer 27

What's -2 times -2?
What's -2 times 2x?
What's -2 times (-2+2x)?

Answer 28

4 + 4x

Answer 29

Wouldn't that be 4-4x?

Answer 30

oh yeah true

Answer 31

Given 3x - 2( y )= 11, replace -2(y) with your 4-4x.

Answer 32

3x (4 - 4x) = 11

Answer 33

Missing sign. 3x +4 -4x = 11
Combine 3x -4x.
Move that '4' to the right side (use subtraction to do that).

Answer 34

x - 4x = 11

Answer 35

Have to subtract 4 from BOTH sides: 3x-4x = 11-4
Simplify this. Find x.

Answer 36

so.. 3x - 11?

Answer 37

3x-4x is -x, and 11-4 is 7.

You should end up with -x=7. Solve this for x.

Answer 38

well -7

Answer 39

x=-7.

Answer 40

yes..

Answer 41

Next, we have to find the value of y.
The 2nd equation is 3x - 2y = 11.
Replace "x" here with (-7). Be sure to include those parentheses. Find y

Answer 42

-21 - 2y = 11

Answer 43

Very good. Must now solve this for y.
To do this, please ADD 21 to both sides of the equation.

Answer 44

so -2y = 31?
or -21 + 19 = 11

Answer 45

-21 - 2y = 11
+21 =+21
-----------------

0 -2y = 32

find y

Answer 46

-16

Answer 47

Correct!

Sorry this discussion seems so long.
I am going to go thru this problem really quickly:

{2x - y = 2
3x - 2y = 11

Solving the first eq'n for y, -y=2-2x, or y=2x-2.

Subbing this last result into the 2nd equation, 3x-2(2x-2)=11

Answer 48

3x-4x+4=11
-x =7, or x=-7

Answer 49

Just wanted to show you how fast this goes once we've gotten the hang of it.

Answer 50

{2x - y = 2
3x - 2y = 11

2nd equation is 3x-2y=11. Find y. Subbing x=-7, 3(-7) - 2y = 11
-21 -2y = 11
y=-16

Solution is ( x , y)

Please write in the values of x and y that we've just found.

Answer 51

solution is (

Answer 52

(-7, -16)

Answer 53

Cool. Done.
Questions?

Answer 54

no for now no imma need to look over what we did and thank you :)

Answer 55

We were using the .... method. Can you remember?

Answer 56

substitution right

Answer 57

yes, right! good! we subbed y=-4+4x.

Good for you!

Til later, then, bye.