Problem 43
Question
How do you determine whether a given ordered triple is a solution of a system in three variables?
Step-by-Step Solution
Verified Answer
To determine whether a given ordered triple is a solution for a system of three variables, substitute the values from the ordered triple into the system of equations. If all equations hold true, it's a solution.
1Step 1: Identify the ordered triple and system of equations
The first step in the process is to identify the ordered triple presented in the problem. An ordered triple would typically be in the format of (x, y, z). Additionally, identify and comprehend the system of equations that is going to be analyzed.
2Step 2: Substitute values from ordered triple into system of equations
In the second step, substitute the values from the ordered triple into the system of equations. That means, wherever a variable appears in the system of equations, replace it with the corresponding value from the ordered triple.
3Step 3: Verify if equations are true.
Next, after substituting the values into the equations, simplify each equation. If all simplified equations are valid (the left-hand side equals to right-hand side), then the given ordered triple is a solution to the system. If any of the equations don't hold true, then it isn't a solution.
Other exercises in this chapter
Problem 42
In Exercises \(29-42,\) solve each system by the method of your choice. $$ \left\\{\begin{array}{l} x-3 y=-5 \\ x^{2}+y^{2}-25=0 \end{array}\right. $$
View solution Problem 42
In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to
View solution Problem 43
perform each long division and write the partial fraction decomposition of the remainder term. $$ \frac{x^{5}+2}{x^{2}-1} $$
View solution Problem 43
Graph the solution set of each system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}x+y>4 \\\x+y>-1\end{array}\right.$$
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