Question

Select the correct solutions for the system of equations:5x +y= -10y= 2^2 - 2x - 8

Answer 1

Given:

`5x+y=-10`
`y=x^2-2x-8`

We can solve for the value of x through substitution.

We will substitute the value of y from the second equation, to the first equation.

`5x+y=-10`
`5x+(x^2-2x-8)=-10`
`5x+x^2-2x=-10+8`
`x^2+3x=-2`
`x^2+3x+2=0`

We then get the factors of this equation.

(x + 1)(x + 2) = 0

Next, we will solve for the value of x.

`x+1=0`
`x=-1`
`x+2=0`
`x=-2`

With these two values of x, we can now find the values of y through substituting the values of x to either equations.

Using the first equation, given that:

x = -1

x = -2

`x=-1`
`5x+y=-10`
`5(-1)+y=-10`
`-5+y=-10`
`y=-10+5`
`y=-5`

Therefore, this will give us a solution of (-1, -5).

Next,

`x=-2`
`5x+y=-10`
`5(-2)+y=-10`
`-10+y=-10`
`y=-10+10`
`y=0`

And this will give us a solution of (-2, 0).

Therefore, all the possible solutions for this system of equations are (-1, -5) and (-2, 0).