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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

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Procrastinator1
I couldn't put the other graph but they both the intersected at (5,0)
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Answer:

Given the system of equation:

[tex]y = x^2-2x-15[/tex]          .....[1]

[tex]y=8x-40[/tex]                 ......[2]

Equate these two equations we get;

[tex]x^2-2x-15 = 8x-40[/tex]

Subtract 8x to both sides we have;

[tex]x^2-10x-15 =-40[/tex]

Add 40 to both sides we have;

[tex]x^2-10x+25 =0[/tex]

Using the identity rule:

[tex](a-b)^2 =a^2-2ab+b^2[/tex]

then;

[tex](x-5)^2 = 0[/tex]

⇒[tex]x-5 = 0[/tex]

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)

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