Solve the system by substitution

-x - y - z = -8
-4x + 4y + 5z = 7
2x + 2z = 4

 The required solution of the given system is

x = 3, y = 6 and z = -1.

Step-by-step explanation:  We are given to solve the following system of equations by the method of substitution :

From equation (iii), we have

Substituting the value of x from equation (iv) in equations (i) and (ii), we get

and

From equation (iii), we get

Thus, the required solution of the given system is

x = 3, y = 6 and z = -1.

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.