Question

Solve the system using substitution and describe your steps
x = y - 3
2x + y = 12

Answer 1

the first equation (x = y - 3) tells us that we can replace x with y - 3 whenever we see it, right?

look at the second equation, replace x with (y-3) and solve for y

then go back and solve for x using the first equation

Answer 2

i need more help

Answer 3

does this make sense? see how we replace "x" with (y-3)?

Answer 4

is that the final answer?

Answer 5

no, but do you understand so far?

Answer 6

yes

Answer 7

ok, so we have 2(y-3) + y = 12, so what do you get when you distribute the 2?

Answer 8

where do u distribute it to

Answer 9

this is a new concept

Answer 10

2(y-3) = 2*y-6

Answer 11

excellent, so far we have 2y - 6 + y = 12, so combine like terms to find y

Answer 12

3y-6=12

Answer 13

getting there, now add 6 to both sides and divide by 3 to find y

Answer 14

6

Answer 15

great, so we know that y = 6, but we're still not done yet because we need to find x

from the first equation, we know that x = y - 3, and since y = 6, what is x?

Answer 16

3?

Answer 17

good! x = 3 and y = 6

generally, the solution to a system of equations is written as (x,y), so since x = 3 and y = 6, our solution is (3,6)

that's our final answer

Answer 18

thank you