Question

Solve the following system by substitution.
7x + 2y = 16
–21x – 6y = 24

Answer 1

I wanna try it out and just let me know if i go wrong :)

Answer 2

Go for it. You can do it.

Answer 3

Solve the following system by substitution.
7x + 2y = 16
-21x - 6y = 24
Start by isolating y

Answer 4

Wait O_O I forgot how to do these

Answer 5

do you have to do it by substitution or can u use any method?
because elimination would be easier

Answer 6

Isolate either variable (x or y) in either one of the equations. Choose whichever looks the easiest.

Answer 7

ok so if i subtracts 7x?

Answer 8

In the first equation? Go for it.

Answer 9

2y=-7x+16 i dont know what to do after that? I mean would I divide by 2?

Answer 10

That's right. Then you'll have an expression for y that you can substitute into the other equation. By the way, this problem will be a little trickier that the last one. But you can do it!

Answer 11

hahah thanks :) and i think i would get y = –( 7/2 )x + 8

Answer 12

Don't forget the negative sign on the 7/2 x

Answer 13

right so y=-7/2x+8?

Answer 14

Great. Now substitute this expression for y into the other equation. Simplify and solve for x.

Answer 15

–21(-7/2x+8) – 6y = 24

Answer 16

Sorry. You substituted for x again. Remember the expression -7/2 x+8 is the expression for y and is substituted in place of y, not x

Answer 17

ugh lol i feel like im never gonna get this >_<
–21x – 6(-7/2x+8)=24?

Answer 18

Exactly. You got it. Now solve for x. I should warn you that there's a surprise coming up in this question, but it's a great learning opportunity.

Answer 19

Don't forget the negative signs where they appear.

Answer 20

lol suprise hehe ok umm... 6(-7/2x+8)=24
im confused O_o

Answer 21

Wait. you should now have\[-21x-6\left( -\frac{ 7 }{ 2 }x+8 \right)=24\]Multiply through by the 6 and simplify.

Answer 22

See where we substituted for the y?

Answer 23

-21x-21x-48=24?

Answer 24

That's it exactly. Now simplify and what do you get?

Answer 25

Oops. There's an error with one of the signs. Double check you last result.

Answer 26

-21x+21x-48=24?

Answer 27

That's better. Now simplify. What do you end up with?

Answer 28

-21x-21x=72??????? is that even possible O_O

Answer 29

What is -21x+21x?

Answer 30

42?

Answer 31

Just combine -21x and 21x. What do you get?

Answer 32

42 right?

Answer 33

42x?

Answer 34

Nope\[-21x+21x=?\]

Answer 35

0

Answer 36

Right on. So, you had\[-21x+21x-48=24\]Simplify the left hand side.

Answer 37

x=78?

Answer 38

What is -21x + 21x again?

Answer 39

0

Answer 40

Subtract 48 = ?

Answer 41

-48

Answer 42

Right. So Everything you've done has come down to\[-48=24\]Is this possible?

Answer 43

no you would get a fraction =/

Answer 44

SURPRISE!! Your work is correct. The problem is the question. There is no solution to that system of equations.

Answer 45

:OO all dis work for nothing

Answer 46

I hear you. But take heart. What you've done is valuable. The process is always the same when solving by substitution. Solve one of the equations for one of the variables (doen's matter which...choose what looks easiest). Then substitute the resulting expression into the OTHER equation. You will then be able to solve that equation for one of the variables. Substitute that value into either of the original equations to solve for the other variable.

Answer 47

haha i get you thanks so so much <3 :D

Answer 48

Feel like trying one that does have a solution? I could give you one.

Answer 49

haha sure :)

Answer 50

Ok. Solve\[2x+3y=13\]\[4x-2y=2\]

Answer 51

ok so first I should add 2x right?

Answer 52

no subtract 2x

Answer 53

3y=-2x+14 divide by 3?

Answer 54

For the first equation? Sure. But, there's a 13 in that equation, so you'll end up dealing ith fractions. Do you think it might be easier to work with the second equation?

Answer 55

yes so 4x−2y=2 add 4x
-2y=-4x+2
divide by -2
y=-2x-1

Answer 56

Terrific. The lesson hear is that it's worthwhile taking a second to look at each equation carefully and choosing which will be easier to work with. You can save yourself a lot of work. Now substitute this expression for y into the other equation.

Answer 57

7x + 2y = 16
7x+2(2x-1)=16
7x+4x-2=16
11x-2=16
11x=18
and im stuck >_<

Answer 58

You're using the wrong equation. You should be substituting into 2x+3y=13.

Answer 59

oh i feel stupid now :(
2x+3(2x-1)=13.
2x+6x-3=13
8x-3=13
8x=16
divide by 8
x=2 :D

Answer 60

Excellent. Know what to do next?

Answer 61

sub into the other problem right?

Answer 62

Go for it.

Answer 63

7x + 2y = 16
7(2)+2y=16
14+2y=16
2y=2
y=1 :D

Answer 64

Wrong equation again. Give it one more try. Either of the two equations I gave you.

Answer 65

I got confused from the previous problem
2x+3y=13
2(2)+3y=13

Answer 66

is that right so far?

Answer 67

Yes.

Answer 68

4+3y=13
3y=9
y=3?

Answer 69

Bravo! You must be exhausted! But you are now able to solve systems of two linear equations in two unknowns by substitution. Way to go, champ!

Answer 70

Hahaha thank you so much I actually get this I appreciate your efforts your awesome <3

Answer 71

Any time.