What is a second linear equation to create a system that has exactly one solution for 3x+9y=-8

Any line with a different slope than the one you start with will intersect that line exactly once, having one solution...

9y=-3x-8

y=-x/3 -8  so you can make any line imaginable and it will have one intersection with this line as long as it has a different slope, not -1/3.

Answer

1 number

explanation

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.

The answer would be $68.04