If you graphed this system, what would the solution be?

y=2x
y=−1x−6

(-2, -4)

Step-by-step explanation:

[y = 2x, y = -x -6]

Solve by substitution:

-x - 6 = 2x

simplify

3x = -6

divide

x = -2

Plug back in one equation to solve for y coordinate:

y = 2(-2)

y = -4

(-2, -4)

47 - 90 = 43

43 - 180 = x

x = 137

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.