Question

Which represents the solution(s) of the system of equations, y = x2 – 2x – 15 and y = 8x – 40? Determine the solution set algebraically. (–5, –80) (5, 0) (5, 0) and (–5, –80) no solutions

Answer 1

I couldn't put the other graph but they both the intersected at (5,0)

Answer 2

Given the system of equation:

`y = x^2-2x-15` .....[1]

`y=8x-40` ......[2]

Equate these two equations we get;

`x^2-2x-15 = 8x-40`

Subtract 8x to both sides we have;

`x^2-10x-15 =-40`

Add 40 to both sides we have;

`x^2-10x+25 =0`

Using the identity rule:

`(a-b)^2 =a^2-2ab+b^2`

then;

`(x-5)^2 = 0`

⇒
`x-5 = 0`

Add 5 to both sides we have;

x = 5

Substitute this value in [2] we have;

y=8(5)-40 = 40-40 = 0

therefore, the solution(s) of the system of equations is, (5, 0)