Question

solve the following system of equations x^2+y^2=136/9
y-3x=8/3

Answer 1

There's a few ways to do this Problem.
First you can solve the second equation for Y
Then substitute y= 8/3+3x into the first equation.

Answer 2

which gives you x^2+(8/3+3x)^2=136/9. Expand the parenthesis, combine like terms, then solve for X

Answer 3

how would you expand the parenthesis?

Answer 4

\[(\frac{8}{3}+3x)*(\frac{8}{3}+3x)\] then Use FOIL to multiply.

Answer 5

so would you get 64/9+16x+9x^2 ?

Answer 6

Yes, exactly. Now you can combine the like terms. Then to solve for X, set the equation =0 and factor. You may have to use the Quadratic Formula to factor. Let me check

Answer 7

x=2/5 and x=-2 ?

Answer 8

Yes, those are the values of X. Now test for both values, by plugin them back into one of the original equations. I'd suggest use the second one, it might be simpler.

Answer 9

In some cases, one of the values might not be in the domain of the system, so you always have to check all of them

Answer 10

so the answers would be (2/5,58/15) and (-2,-10/3)

Answer 11

right?

Answer 12

Srry, yes those are the points

Answer 13

Thank You!!

Answer 14

No Problem :)