Hardest question ever omg! (that was my stereotypical teenage girl impression) ; )

solve the following system using the substitution, elimination, or graphing method for the y coordinate.
x= -4y+3
-x-4y=-3

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.