Question

Linear and Nonlinear systems of equations. Solve the system with substitution.
-(1/2)x+y=-(5/2)
x^2+y^2=25

Answer 1

What's the question? Solve for x and y?

Answer 2

Oh I see it says substitution :P

Answer 3

My bad :X, updated the question.

Answer 4

Alright, so lets solve for y in the linear equation and plug it into the equation of circle they gave you

Answer 5

Any idea how?

Answer 6

\[y = -\left( \frac{ 5 }{ 2 } \right) + \left( \frac{ 1 }{ 2 } \right)x\] right?

Answer 7

Yea sorry, I'm still here. Ok

Answer 8

Now lets plug that into the second equation, can you do that?

Answer 9

Ok, I gotten \[x ^{2}+(\frac{ 1 }{ 2 }x)-\frac{ 55 }{ 2 } =0\]. Then we use the quadratic equation right to find the two X's?

Answer 10

\[x^2+ \left( -\frac{ 5 }{ 2 }+\frac{ 1 }{ 2 }x \right)^2=25\] this is what you get when you plug it in right

Answer 11

Not sure what you're doing

Answer 12

\[\left( -\frac{ 5 }{ 2 } +\frac{ 1 }{ 2 }x\right)\left( -\frac{ 5 }{ 2 } +\frac{ 1 }{ 2 }x\right)\] you need to expand this :), and no worries

Answer 13

\[x ^{2}-\frac{ 25 }{ 4 }+\frac{ 1 }{ 4 }x ^{2}\]. That next step?

Answer 14

You should get \[\frac{ x^2 }{ 4 }-\frac{ 5x }{ 2 }+\frac{ 25 }{ 4 }\]

Answer 15

\[x^2+\frac{ x^2 }{ 4 }-\frac{ 5x }{ 2 }+\frac{ 25 }{ 4 } = 25\] this is what you should have now

Answer 16

\[x ^{2}-\frac{ 25 }{ 4 }+\frac{ 1 }{ 4 }x ^{2} -> (\frac{ 4 }{ 4 }x ^{2}+\frac{ 1 }{ 4 }x ^{2})=5x ^{2}-\frac{ 25 }{ 4 }=25\]

Answer 17

Check your work

Answer 18

And signs

Answer 19

How do you get \[\frac{ x ^{2} }{ 4 }-\frac{ 5x }{ 2 }+\frac{ 25 }{ 4 }\]?

Answer 20

\[\left( -\frac{5 }{ 2 }+\left( \frac{ 1 }{ 2 }x \right) \right)^2 \implies (\left( -\frac{5 }{ 2 }+\left( \frac{ 1 }{ 2 }x \right) \right)\left( -\frac{5 }{ 2 }+\left( \frac{ 1 }{ 2 }x \right) \right)\]

Answer 21

Yeah it's a messy question :P don't worry all I did was "foil"

Answer 22

Yea I'm working on it still, the answer on the book shows (-3,-4) and (5,0). So, I'm figuring out how to get those at the moment.

Answer 23

We will have to factor we're almost at that process

Answer 24

But tag me if you have anymore troubles good luck!

Answer 25

Yea, thanks for your time.

Answer 26

Np!