Which of the following ordered pairs are solutions to the system of equations below? (3x + 5y = 14
y = 1/2x + 5)
O (2.4)
0 (-2,4)
O (2,6)
O (-2,6)

(- 2, 4 )

Step-by-step explanation:

Given the 2 equations

3x + 5y = 14 → (1)

y = x + 5 → (2)

Substitute y = x + 5 into (1)

3x + 5( x + 5) = 14

3x + x + 25 = 14

x + 25 = 14 ( subtract 25 from both sides )

x = - 11 ( multiply both sides by 2 )

11x = - 22 ( divide both sides by 11 )

x = - 2

Substitute x = - 2 into (2) for corresponding value of y

y = × - 2 + 5 = - 1 + 5 = 4

solution is (- 2, 4 )

312312

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: