Question

How do you solve a system where both equations are the equivalent of y?

y = 2x – 12
y = -x + 3

Answer 1

set their "right hand sides" equal to each other, then simplify

Answer 2

@Phi
How would you do that

Answer 3

do you see the right hand side of
y = 2x – 12
?

it is
2x -12

set that equal to the right hand side of the other equation

Answer 4

can you write down the equation you get when you set the "right hand sides" equal to each other? (Don't solve it, just write it down)

Answer 5

Oh okay

Answer 6

can you write down the equation?

Answer 7

Yeah 2x-12
-x=3

Answer 8

you mean -x+3 on the second line, right?
put them on the same line, and put an = between them
can you do that ?

Answer 9

Yeah I meant plus 2x-12=-x+3

Answer 10

yes, that looks good.
one way to think of this is
y = 2x – 12 is (in a way) like saying "the weight of y" is the same as the "weight of 2x - 12"

the other equation
y = -x + 3 says "the weight of y" is the same as the weight of -x +3

Now we use common sense: if -x + 3 weighs the same as y, and 2x-12 weighs the same as y, then it makes sense that -x+3 weighs the same as 2x-12

we write
2x-12=-x+3

Answer 11

to solve, we add numbers (or letters) to both sides (to keep things equal)
think of a balance (or scales or a teeter-totter), where you have weight on both sides, and things are balanced.

Answer 12

for example add +12 to both sides. Just write +12 on both sides
2x-12=-x+3

add +12 to both sides
2x - 12 + 12 = -x + 3 + 12

Answer 13

now simplify the equation
2x - 12 + 12 = -x + 3 + 12

on the right side you have 3+12. can you simplify that to one number ?

Answer 14

15

Answer 15

ok, now you have

2x - 12 + 12 = -x + 15

what about on the left side? what is -12 + 12 ?

Answer 16

those would cancel out so 0

Answer 17

so you would be left with 2x=-x+15

Answer 18

yes. Now we use the same idea, but with the letters
add 1x to both sides

2x + 1x = 1x - 1x + 15 (when they write -x that is the same as -1x)

on the left side you have 2 x's and add 1 more x's
how many x's do you have ?

Answer 19

you'd have 3 x's

Answer 20

and on the right side we have what ?

Answer 21

They'd cancel out so we'd be left with 15

Answer 22

so now we have
3x = 15

last step. we use the idea that anything divided by itself is 1
Here, we divide 3 by 3. And we have to do the same thing to the other side to keep things balanced

3x/3 = 15/3

on the left 3/3 = 1
1x = 15/3
or (because we don't bother to write the 1 when we have 1x)
x = 15/3

simplify the right side, and we get the final answer.

Answer 23

So x equals 5

Answer 24

yes

Answer 25

Alright thanks

Answer 26

yw