Question

Solve using substitution
x/3+y/5=1 x+6y=12

Answer 1

You can make that first equation a little more palatable to work with by multiplying it by 15.

Answer 2

Then if you multiply it by 2 and subtract it from the second equation, you can get y to eliminate and you'll have a solution for x.

Answer 3

Hi Cliff,
quick question, when you solve it in the manner you suggest, is that solve by elimination?

Answer 4

i need to solve by substitution!

Answer 5

@hugo, yes, I suppose it is.

Answer 6

In that case, I still recommend multiplying the first equation by 15 to clear the fractions, then solve the first equation for y, and the second equation for x, then do a substitution.

Answer 7

so if i do heres what i did so far
\[ \frac{ x }{ 3 }+\frac{ y }{ 5} = 1 \]
\[x+6y=12 \]
so solved for x and got x=12-6y ?

Answer 8

yes, that sounds good.

Answer 9

Ok, now if you multiply the first equation by 15, you'll get
5x + 3y = 15

Answer 10

then i would have to type in for x/3 as 12-6y/3 +y/5 = 1 ?

Answer 11

so now if I take you first equation ninab and substitute into Cliff's I get:
5 (12 - 6 y) + 3y = 15
Can you take it from there?

Answer 12

ya

Answer 13

60-30y+3y=15
60-27y=15 ?

Answer 14

yes, looks right so far

Answer 15

so then subtract 15 from both sides i get 45=27y

Answer 16

so y=5/3

Answer 17

That seems right. So what about x?

Answer 18

x=2

Answer 19

thank you both @CliffSedge and @Hugo47

Answer 20

So since you had two equations, your solution is an ordered pair in the form (x,y)
So (2, 5/3).