Question

What is the value of x in the solution to the following system of equations?

x − y = −3
x + 3y = 5

Answer for Blank 1:

Answer 1

@Vocaloid

Answer 2

since you have -y in the first equation and +3y in the second equation

try multiplying the first equation by 3, adding the equations together, then solving for x

Answer 3

what do you mean by multiplying the first equation by three? @Vocaloid do you mean multiply 3 by -3?

Answer 4

you can multiply both sides of the equation by 3

3(x − y) = 3(−3)

then distribute

Answer 5

okay

Answer 6

so i got -9

Answer 7

don't forget about the left side

3(x-y)

what do you get when you distribute this?

Answer 8

you get 3x-3y

Answer 9

awesome

so 3x - 3y = -9

combine that with our original equation to get the new system

3x - 3y = -9
x + 3y = 5

now try adding the two equations together

Answer 10

okay

Answer 11

im a tad confused

Answer 12

take it one set of variables at a time

notice how one equation has x and the other has 3x

so x + 3x = ?

Answer 13

5

Answer 14

hm, not quite. notice how we have one x + three x

if 1 + 3 = 4 what might x + 3x = ?

Answer 15

im not sure this one is really confusing me im sorry hm

Answer 16

well think of the x's as just ordinary objects

1 object + 3 objects = 4 objects
x + 3x = 4x

Answer 17

using that same logic, let's go onto the y terms

any ideas what -3y + 3y = ?

Answer 18

0?

Answer 19

awesome

so finally we have -9 + 5 which is just -4

so

4x = -4

any ideas what x might be equal to?

Answer 20

-1?

Answer 21

yup, so -1 is your solution

Answer 22

wow thank you so much! @Vocaloid