Question

Please help me!
Solve by substitution. Show each step of your work.

2x + y = 7

3x + 5y = 14

Answer 1

To substitute, we need to set these equations equal to each other. How would we do that?

Answer 2

We need to make them become one somehow.

Answer 3

I think we do to through combining like terms.

Answer 4

*it

Answer 5

Right, lets try to get the y's by themselves

Answer 6

Like the first, how would you get the 2x by itself

Answer 7

Subtract it from both sides.

Answer 8

Right, so we have y = 7 - 2x. I recommend organizing it to y = -2x + 7

How about the second one?

Answer 9

For the second one, we need to subtract 3x from both sides. Does that mean we will have 5y = -3x + 14?

Answer 10

Exactly ^

But we want to get y by itself, so what would we do to get that 5 away from the y?

(You did the opposite by subtracting a positive number, so the opposite of multiplication would work)

Answer 11

We should divide by 5.

Answer 12

Yes, so that would give you y = -3x + 14
--------
5

So, now we want to set the two equations equal to each other, so you would get the first equation we found, put an equal sign, then put the second equation we found

Answer 13

So, what are we supposed to do next?

Answer 14

Alright, so setting them equal makes ite
(-2x+7) = -3x + 14
--------
5

So, the tedious part is, we have to do this one more time... get the numbers with x's and the numbers with no x's away from each other

Answer 15

As a quick run-through, I see you can, So basically you would multiply 5 on each sides, right? Since you're dividing by 5 to get

(-10x + 35) = (-3x +14)

Would you know the equation after getting the X variables and the whole numbers alone on each side?

Answer 16

I believe we could figure it out after that, but I don't know how to make the x variable and the whole numbers on their side alone.

Answer 17

You would do like the last step

Note: Whole numbers are different from whole numbers with variables

So for the left side, how would we get a ~~Positive~~ 35 to the other side?
And for the right side, how would we get a ~~Negative~~ 3x to the other side?

Answer 18

I guess we need to bring the 35 over through addition and the 3x to the other side through subtraction.

Answer 19

Almost, they are flipped. You would subtract 35 since it's the opposite of positive and add 3x since it's negative

Doing that gives you:

-7x = 21

Now we solve for x, to get the x value to the actual answer

Answer 20

P.S. -- This seems long af, but it's not lol once you get the concept rolling

Answer 21

Okay, so x = -3 because -7 times -3 is positive 21.

Answer 22

Yes! That -3 is the x value using substitution.

Now, we have to do one last step. We have to plug in -3 for x for each of the equations you stated in your original question and solve for y

If the y value comes out to be the same for each equation, then we did this problem correctly

Answer 23

Aw damn, x is suppose to be 3, not -3

Answer 24

Because when you subtract 35 from each side, you get 14-35 which is -21 not +21, so it comes out to -7x=-21.. that's my fault

Answer 25

Well, I'll try with three this time.

2x + y = 7
3x + 5y = 14

2(3) + y = 7
3(3) + 5y = 14

6 + y = 7
9 + 5y = 14

6 + 1 = 7
9 + 5(1) = 14 .................. 9 + 5 = 14

That's correct then! y = 1

Answer 26

Yep! So through substitution, which it tedious

x = -3, y = 1

Good job homie or homegurl, whichever one lol

Answer 27

Thank you for your help. Otherwise, I would have been here for ages.

Answer 28

No problem! This one was more complicated, since both x and y were missing. Anytime tho!