Question

Solve the system algebraically: y = sqrt(x) and y=2x

Answer 1

Could I help you?

Answer 2

Yes please

Answer 3

Thank you.
With my pleasure!


Do you like to do so by substitution or elimination?

Answer 4

I started doing substation on it and got 2x = sqrt x but then I blanked out on what to do next.

Answer 5

substitution*

Answer 6

Both of them are y terms. Basically, set the two equations equal to each other.
sqrt(x) = 2x

Answer 7

I have that so far, but after that how would I solve it? Sorry, I'm blanking out on how to do the basics.

Answer 8

We can use either substitution where we plug one equation into the other, or elimination where we combine the equations.

Answer 9

\[\large \sqrt x = 2x\]you can square both sides of the equation to get rid of the square root\[\large (\sqrt x)^2=(2x)^2\]\[\large x = 4x^2\]\[\large 4x^2-x = 0\]
Now do you think you can solve for x now?

Answer 10

Would I need to do the quadratic formula?

Answer 11

Sure, but you can always factor it since it's easier that way.\[\large x(4x-1) = 0\]\[\large x=0, ~~ x=\frac{ 1 }{ 4 }\]

Answer 12

Oh yeah, you're completely right. And then after than I plug in the x's to find the y's right?

Answer 13

Yup, nice work!

Answer 14

Thanks for the help!

Answer 15

You're welcome!