Question

Solve the system of equations y = 2x^2 + x – 6 and y = 4

Answer 1

Explanation:

Substitute y = 4 into the first equation:

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

Subtract 4 from both sides:

`2x^2+x-10=0`

We can factor in order to find values of x.

Factor the equation:

`2x^2+x-10=0`

Factors of 10 we'll use:

5 and 2.

`(2x+5)(x-2)=0`

Set the parentheses equal to 0 then find the values of x:

`(2x+5)=0`

`x=-2(1)/(2)`

`(x-2)=0`

`x=2`

`x=2, \: or \: -2(1)/(2) .`

Check:

`4=2(2)^2+2-6`

`4=2(4)+2-6`

`4=4 \: \checkmark`

`4=2(-2(1)/(2) )^2-2(1)/(2) -6`

`4=2(6(1)/(4))-2(1)/(2) -6`

`4=12(1)/(2) -2(1)/(2) -6`

`4=10-6`

`4=4 \: \checkmark`