Question

Can someone please check my work? Please? I would really appreciate it...
Question~
Solve the systems using the substitution method.
y = (2/3)x + 1
y + x = 6

Answer 1

My Answer~
Solve one equation for either variable ~
Y+x=6
In the other equation, replace the variable from S1 with what it equaled
(2/3)x+1+x=6
Solve the equation in step 2 for the other variable:
Multiply both sides by 3 to clear the fraction~ 3(2/3)x+1+x=6*3
Combine like terms~ 2x+3+3x=18
Subtract 3 from both sides~ 5x+3-3=18-3
Solve for x ~ 5x=15
Write your answer as an ordered pair (x, y).
(3,3)

Answer 2

What my teacher said was wrong~
What is this?
Solve one equation for either variable ~
Y+x=6
=
the rest of your steps don't make sense to me. can you help me?

Answer 3

you got the answer correct. . .

Answer 4

You start by saying
Solve one equation for either variable

then you write down the 2nd equation. But I would write down the first equation
y = (2/3)x + 1

because "solve for a variable" means have the variable by itself on one side of the = sign.
In the first equation y is by itself on the left side. In other words, the first equation is already "solved for y". So I would start by saying

1. Solve one equation for either variable. We use equation 1 because it is already solved for y:
y = (2/3)x + 1

Answer 5

Then I would say
2. In the other equation,
y+x= 6
replace the variable y with what it equaled. The new equation is
(2/3)x+1+x=6

Answer 6

Next step, the easiest thing to do is add -1 to both sides
3. simplify the equation by adding -1 to both sides. It is
(⅔) x + x = 5

next, you can multiply both sides by 3 (to get rid of the fraction)
or you can add ⅔ x + 3/3 x = 5/3 x

But let's multiply by 3:

4. Multiply both sides by 3
2x+3x = 15

5. combine like terms
5x= 15

6 divide both sides by 5
x=15/5
x= 3

7. Use either equation to solve for y. the first equation, with x=3 is
y = (⅔)*3 + 1
y= 2+1
y=3

Answer 7

Your write-up is mostly ok. Did your teacher not like it ?

Answer 8

I guess she didn't, but I have done many other answers like the one I posted... Thank you so much for showing me how I should write the steps!! You're amazing!!