Question

can someone help me solve this either using substitution or elimination please?
1/2x + 2/3y = 6
x + y = 10

Answer 1

You can change the first equation by multiplying it by 6 and this will get rid of the fractions....
(6)1/2x + (6)2/3y = (6)6
3x + 4y = 36 (thats better)
x + y = 10 --> x = 10 - y

now sub 10 - y in for x in the " new equation ".

3x + 4y = 36
3(10 - y) + 4y = 36

Can you finish it from here ?

Answer 2

Okay , I was making sure I was on the right track, I managed to eliminate the fractions. What I am having trouble with is the second equation

Answer 3

Which equation is "the second equation" in your eyes, and what is the trouble you are having? Can you show us your work so far?

Answer 4

the x+y=10

Answer 5

what i have is
6*1/2x+6*2/3y=6
3x+4y=36

Answer 6

and I get that x=4, and y=6?

Answer 7

Well, let's check those out: they have to satisfy both equations to be a valid solution to the system:

\[x+y=10\]
\[4+6=10\checkmark\]
\[\frac{1}{2}x+\frac{2}{3}y =6\]\[\frac{1}2(4)+\frac{2}3(6) = 6\]\[2+4=6\checkmark\]Good work!

Answer 8

o wow, so I had it correct? lol

Answer 9

It's important to check both equations: if you'd made an error somewhere along the line and gotten x=3, y = 7, that would satisfy one equation, but not the other.

Answer 10

Do you want to try doing it by elimination now?

Answer 11

I can try