Chapter 11: Q. 16 (page 714)

Verify that the values of the variables listed are solutions of the system of equations.
$\{\begin{matrix} \begin{array}{rcl} 4 x - 5 z & = & 6 \\ 5 y - z & = & - 17 \end{array} \\ - x - 6 y + 5 z = 24 \end{matrix} x = 4, y = - 3, z = 2; (4, - 3, 2)$

Short Answer

Expert verified

The given values are the solutions because all equations are true for the given values.

Step by step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl} 4 x - 5 z & = & 6 \\ 5 y - z & = & - 17 \\ - x - 6 y + 5 z & = & 24 \end{array}$

The given solution is $x = 4, y = - 3, z = 2$ or $(4, - 3, 2)$ .

Step 2. Check the solution.

If all equations are true for the given values, then the values represent the solution.

Substitute $x = 4, y = - 3, z = 2$ in the first equation.

$\begin{array}{rcl} 4 (4) - 5 (2) & = & 16 - 10 \\ = & 6 \end{array}$

So, the first equation is true.

Substitute $x = 4, y = - 3, z = 2$ in the second equation.

$\begin{array}{rcl} 5 (- 3) - (2) & = & - 15 - 2 \\ = & - 17 \end{array}$

So, the second equation is true.

Substitute in the third equation.

$\begin{array}{rcl} - (4) - 6 (- 3) + 5 (2) & = & - 4 + 18 + 10 \\ = & 24 \end{array}$

So, the third equation is true.

Step 3. Conclusion.

The given values are the solutions because all equations are true for the given values.

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Verify that the values of the variables listed are solutions of the system of equations.
$\{\begin{matrix} \begin{array}{rcl} 4 x - 5 z & = & 6 \\ 5 y - z & = & - 17 \end{array} \\ - x - 6 y + 5 z = 24 \end{matrix} x = 4, y = - 3, z = 2; (4, - 3, 2)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check the solution.

Step 3. Conclusion.

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Verify that the values of the variables listed are solutions of the system of equations.4x-5z=65y-z=-17-x-6y+5z=24x=4,y=-3,z=2;4,-3,2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check the solution.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Discrete Mathematics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Verify that the values of the variables listed are solutions of the system of equations.
$\{\begin{matrix} \begin{array}{rcl} 4 x - 5 z & = & 6 \\ 5 y - z & = & - 17 \end{array} \\ - x - 6 y + 5 z = 24 \end{matrix} x = 4, y = - 3, z = 2; (4, - 3, 2)$