How do you solve the system x+2y=13 and −2x−3y=−18 using substitution?

2 Answers
Andy Y.
May 29, 2017

x=−3 and y=8

Explanation:

Starting with x+2y=13, get x by itself on the left-hand side by subtracting 2y from both sides.

x=−2y+13

This gives us a new name for x, which we can plug back in to

−2x−3y=−18

−2(−2y+13)−3y=−18

4y−26−3y=−18

Combine the terms with y

y−26=−18

Add 26 to both sides.

y=8

Now plug y=8 back into one of the two equations with both x and y still in it from above.

x=−2y+13

x=−2(8)+13

x=−16+13

x=−3

ANSWER: x=−3 and y=8

Izzy H. · Stefan V.
May 29, 2017

x=−3

y=8

Explanation:

Since,

x+2y=13

Then,

x=13−2y

Substuting [x=13−2y] in the other equation, (−2x−3y=−1), It becomes

−2(13−2y)−3y=−18

Simplify,

−26+4y−3y=−18

Which is the same as:

−26+y=−18

Put y on the left side of the equal sign and actual numbers on the right

y=−18+26

y=8

Go back and solve [x=13−2y] for x, since you now know what y is:

x=13−2(8)

x=13−16

x=−3

Ta da! Please do correct if I'm wrong...
Cheers and all the best!

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