What are the solutions of the following system?

StartLayout Enlarged left-brace 1st row x squared + y squared = 25 2nd row 2x + y = 25 EndLayout
(0, –5) and (–5, 5)
(0, –5) and (5, –15)
(0, –5) and (–4, 3)
(0, –5) and (4, –13)

50

step-by-step explanation:

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.