Olve the system of equations.

{y=3x−7
{15x−5y=14

a. use the substitution method.

b. the solution is (15, 5)

c. the solution is (0, 7)

d. there is no solution.

e. there are an infinite number of solutions.

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.