One more substitution...?

Question

Just once more...could someone show me the steps to solve this system by the substitution method?

x + 3y = 2
-x + y = 1

Answer 1

Sure. Start by picking one of the variables. I am going to pick y. Next choose which equation you want to start with. I am going to use the second equation you wrote because it looks easier. Using the equation that we have chosen, solver for the variable that we have picked.

-x + y = 1

Add x to both sides.

-x + y + x = 1 +x

0x + y = 1 + x

y = 1 + x

Because we will be using this as a substitution, I like to put everything on the right side in parenthesis.

y = (1 +x)

Now for the hard part. Using the OTHER equation, replace y with the result that we just got.

The other equation

x + 3y = 2

Perform the substitution. In other words, put the result we got earlier in place of y.

x + 3(1 + x) = 2

Distribute the 3.

x + 3*1 + 3*x = 2

Collect like terms.

4x + 3 = 2

Subtract 3 from both sides

4x + 3 - 3 = 2 - 3

4x + 0 = -1

4x = -1

Divide both sides by 4

4x/4 = -1/4

x =-1/4

Awesome. Now to find y. Since we already solved for y...

y = 1 + x

All we have to do is put -1/4 in place of x. Be careful since the result we got for x is negative!

y = 1 + (-1/4)

y = 1 - 1/4

y = 4/4 - 1/4

y = 3/4

Hope that helped
10 pts best answer?

Answer 2

x + 3y = 2
-x + y= 1

Solve one of the equations for either x or y. Example:
-x + y = 1
y = x +1

substitute that answer back into Y in the first equation.

x +3(x+1) = 2
x + 3x +3 = 2
4x = -1
x = -1/4

then substitute that back into the second equation:
-(-1/4) +y = (-1/4)
1/4 + y = -1/4
y = -1/2

Hope it helps.

Answer 3

you can do system of equations... or you can do substitution

you want to get a positive variable by itself then plug into the other equation..
x+3y=2
would become x=2-3y
then plug it into the other equation
-(2-3y)+y=1
distrubute the -. -2+3y+y=1
then you want to combine like terms to solve for y.
-2+4y=1
4y=3
y=3/4

then you can plug that back into the back equationt to find x.
x+3(3/4)=2
x+9/4=2 (you can change to decimal to make it easier.. x+2.25=2)
x=-.25