Question

HELP ? Explain how to find the solution to the system below. Then find the solution(s) to the system. Round answers to the nearest hundredth, if necessary.
y=x^2-x-12
y=x

Answer 1

Explanation: Because y = x as given by the second equation, you can substitute it into the first equation ===> you now have 1 equation with only x as variable ==> you can rearrange the terms to solve for x.

Now can you implement that?

Answer 2

how would u rearrange them ?

Answer 3

hmm idk doesn't mean the x stays the same or you add them ?

Answer 4

1?

Answer 5

2?

Answer 6

ohh so it will also equal 1 ?

Answer 7

\( y=x^2-x-12 \)
\(y=x\)

Substitute x in for y in the first equation:

\( x=x^2-x-12 \)

\(x^2 - 2x - 12 = 0 \)

Use the quadractic formula, or complete the square to solve for x.

Answer 8

sorry xoxox123 :(

Answer 9

sorry for what ??? @mth3v4

Answer 10

i have mislead you :P

Answer 11

your good its ok.

Answer 12

ax2 + bx + c = 0" @mathstudent55 so i substuite my numbers into this

Answer 13

To use the quadratic formula?

Answer 14

yes

Answer 15

ax^2

Answer 16

\( x^2 - 2x - 12 = 0\)

\( ax^2 + bx + c = 0\)

\( x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

Use \(a = 1\), \(b = -2\), and \(c = -12\) in the quadratic formula.

Answer 17

-2+ √-2^2-(1)(-12)/2(1) ???????????

Answer 18

Notice the first thing is -b which turns to -(-2) = 2

\(x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-12)}}{2(1)}\)

Answer 19

so what next after u do that

Answer 20

Simplify wherever you can one step at a time until you reach a value for x.

Answer 21

\(x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-12)}}{2(1)}\)

\(x = \dfrac{2 \pm \sqrt{4 - (-48)}}{2}\)

\(x = \dfrac{2 \pm \sqrt{4 + 48}}{2}\)

\(x = \dfrac{2 \pm \sqrt{52}}{2}\)

\(x = \dfrac{2 \pm \sqrt{4 \times 13}}{2}\)

\(x = \dfrac{2 \pm 2\sqrt{13}}{2}\)

\(x = 1 \pm \sqrt{13}\)

Answer 22

cant u simplify any further than that ?

Answer 23

Since the problem wants the answers rounded off, you can do this:

\(x = 1 + \sqrt{13} = 4.61 \)

or

\(x = 1 - \sqrt{13} = -2.61 \)

Remember that this is a system of equations, so you need the solutions as ordered pairs. Since the second equation is y = x, for each value of x, we have a value of y that is equal to it:

The solutions are: (4.61, 4.61) and (-2.61, -2.61)