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

Answer:

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)