Problem 107
Question
If \(x=3, y=2,\) and \(z=-3,\) does the ordered triple \((x, y, z)\) satisfy the equation \(2 x-y+4 z=-8 ?\)
Step-by-Step Solution
Verified Answer
Yes, the ordered triple (\(x, y, z\)) does satisfy the equation \(2 x-y+4 z=-8\).
1Step 1 - Substitute the given values
Substitute \(x=3, y=2, z=-3\) into the equation \(2 x-y+4 z=-8\). The equation becomes \(2*3 -2 +4*(-3) = -8\)
2Step 2 - Simplify the equation
Simplify the expression on the left-hand side: \(6-2-12 = -8\)
3Step 3 - Determine if the equation is valid
The equation is valid if the left-hand side equal to the right-hand side. Here, both sides equals to -8. Therefore, the statement is true.
Other exercises in this chapter
Problem 106
Determine the amplitude, period, and phase shift of \(y=-2 \cos \left(2 x-\frac{\pi}{2}\right) .\) Then graph one period of the function. (Section 5.5, Example
View solution Problem 106
In Exercises \(106-109,\) determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing a linear inequality, I
View solution Problem 107
Determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing \(3 x-4 y
View solution Problem 108
Consider the following equations: \(\left\\{\begin{array}{l}{5 x-2 y-4 z=3} \\ {3 x+3 y+2 z=-3}\end{array}\right.\) Eliminate \(z\) by copying Equation \(1,\) m
View solution