What are the solutions to the system of equations?

B

Step-by-step explanation:

Given the 2 equations

y = 2x² - 5x - 7 → (1)

y = 2x + 2 → (2)

Since both equations express y in terms of x we can equate the right sides, that is

2x² - 5x - 7 = 2x + 2 ( subtract 2x + 2 from both sides )

2x² - 7x - 9 = 0 ← in standard form

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 9 = - 18 and sum = - 7

The factors are + 2 and - 9

Use these factors to split the x- term

2x² + 2x - 9x - 9 = 0 ( factor the first/second and third/fourth terms )

2x(x + 1) - 9(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(2x - 9) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 4.5

Substitute these values into (2) for corresponding values of y

x = - 1 : y = (2 × - 1) + 2 = - 2 + 2 = 0 ⇒ (- 1, 0)

x = 4.5 : y = (2 × 4.5) + 2 = 9 + 2 = 11 ⇒ (4.5, 11)

Solutions are (4.5, 11) and (- 1, 0)

abde or 1,2,4, 5 is the answer

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: