Question

Solve the system of equations.

7x – y = 7
7x2 – y = 7

(0, 7) and (0, –7)
(1, 0) and (0, –7)
(3, 14) and (0, –7)
(4, 14) and (–1, 10)

Answer 1

B. (1, 0) and (0, –7)

Explanation:

I took the algebra exam

Answer 2

2nd option

Explanation:

7x - y = 7 ( multiply through by - 1 )

- 7x + y =- 7 ( add 7x to both sides )

y = 7x - 7 → (1)

7x² - y = 7 → (2)

substitute y = 7x - 7 into (2)

7x² - (7x - 7) = 7 ← distribute parenthesis on left side

7x² - 7x + 7 = 7 ( subtract 7 from both sides )

7x² - 7x = 0 ← in standard form

7x(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

7x = 0 ⇒ x = 0

x - 1 = 0 ⇒ x = 1

substitute these values into (1) for corresponding values of y

x = 0 : y = 7(0) - 7 = 0 - 7 = - 7 ⇒ (0, - 7 )

x = 1 : y = 7(1) - 7 = 7 - 7 = 0 ⇒ (1, 0 )