How to do substitution

Question

X+3y=15 and 2x-3y=-6 in substitution

Answer 1

Just add the 2 equations to get

3x=9

x = 3

then substitute 3 into either equation to calculate y

3y=15-x = 15-3= 12

y = 12/3 = 4

(3,4) is the solution, the point of intersection if you graphed the 2 lines

Answer 2

Hi Caitlin,

There are a couple of ways you could go with that, but let's go the easiest route.

X+3y=15 and 2x-3y=-6

If X + 3Y = 15, subtract 3Y from both sides so you can isolate X.

X + 3Y - 3Y = 15 - 3Y

Now you are left with

X = 15 - 3Y

Because you know this is what X equals, you can "substitute" this into the other equation. Wherever you have an X simply put 15 - 3Y in its place. (The whole purpose of the substitution method)

2X - 3Y = - 6 now becomes

2(15 - 3Y) -3Y = - 6

Multiply to get rid of your parenthesis.

2x15 - 2x3Y - 3Y = - 6

30 - 6Y - 3Y = 6

Combine you Y's

30 - 9Y = - 6

Subtract 39 from both sides

30 - 30 - 9Y = - 6 - 30

Now you are left with

-9Y = -36

Divide both sides by - 9

-9Y ÷ -9 = -36 ÷ -9

and Y = 4.

Now that you know Y = 4, substitute this back into one of your equations and solve for X.

X + 3Y = 15

put your 4 in the place of Y

X + 3 (4) = 15

Multiply your 3 & 4

X + 12 = 15

Subtract 12 from both sides

X + 12 - 12 = 15 - 12

Finish your subtraction and

X = 3

Your solution is X = 3 and Y = 4

Written as (3, 4)

Answer 3

To solve a system of equations by substitution, the first thing that you need to do is solve for either x or y in terms of the other. For this explanation, I'm going to choose x. So:

First, solve for x in terms of y using the first equation:

x+3y=15

x = 15-3y (subtract 3y from both sides)

So we have that x = 15-3y.

Now that we've solved for x, we can plug that in everywhere we have an x in the second equation. This gives us:

2(15-3y)-3y = -6 (plug in)

30-6y-3y = -6 (simplify)

30-9y = -6 (combine like terms)

-9y = -36 (subtract 30 from both sides)

y = 4 (divide by -9)

So we have that y = 4. Now we have to go back to what we found x to be and plug in our new y. So:

x = 15-3y becomes x = 15 - 3(4) = 15-12 = 3.

So x =3. Now that we have our x and our y, we're done with a final answer of x = 3, y = 4