Question

Approximate the solutions to this system.

y=3x^2+x-6
y=x-4
Round your answer to the nearest hundredth.​

Answer 1

`x = \± 0.82`

`y =-3.18 \ or\ -4.82`

Explanation:

Given

`y = 3x^2 + x - 6`

`y = x -4`

Required

The solution

First, we equate both expressions.

`y = y`

`3x^2 + x - 6 = x - 4`

Subtract x from both sides

`3x^2 - 6 = - 4`

Add 6 to both sides

`3x^2 = 2`

Divide both sides by 3

`x^2 = 0.667`

Solve for x

`x = \± \sqrt{0.667`

`x = \± 0.82`

To solve for y, we have:

`y = x -4`

This gives

`y = \± 0.82 - 4`

Split

`y = 0.82 - 4 \ or\ -0.82 - 4`

`y =-3.18 \ or\ -4.82`