Chapter 11: Q. 9 (page 713)

Verify that the values of the variables listed are solutions of the system of equations.
$\{\begin{matrix} 3 x - 4 y = 4 \\ \frac{1}{2} x - 3 y = - \frac{1}{2} \end{matrix} x = 2, y = \frac{1}{2}; (2, \frac{1}{2})$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl} 3 x - 4 y & = & 4 \\ \frac{1}{2} x - 3 y & = & - \frac{1}{2} \end{array}$

The given solution is $x = 2, y = \frac{1}{2}$ or $(2, \frac{1}{2})$ .

Step 2. Check the solution.

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

Substitute $x = 2, y = \frac{1}{2}$ in the first equation.

$\begin{array}{rcl} 3 (2) - 4 (\frac{1}{2}) & = & 4 \\ 6 - 2 & = & 4 \\ 4 & = & 4 \end{array}$

This statement is true.

Substitute $x = 2, y = \frac{1}{2}$ in the second equation.

$\begin{array}{rcl} \frac{1}{2} (2) - 3 (\frac{1}{2}) & = & - \frac{1}{2} \\ 1 - (\frac{3}{2}) & = & - \frac{1}{2} \\ - \frac{1}{2} & = & - \frac{1}{2} \end{array}$

This statement is true.

Step 3. Conclusion.

The given values are the solutions because both 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.
$\{\begin{matrix} 3 x - 4 y = 4 \\ \frac{1}{2} x - 3 y = - \frac{1}{2} \end{matrix} x = 2, y = \frac{1}{2}; (2, \frac{1}{2})$

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.3x-4y=412x-3y=-12x=2,y=12;2,12

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

Applied Mathematics

Discrete Mathematics

Decision Maths

Calculus

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Verify that the values of the variables listed are solutions of the system of equations.
$\{\begin{matrix} 3 x - 4 y = 4 \\ \frac{1}{2} x - 3 y = - \frac{1}{2} \end{matrix} x = 2, y = \frac{1}{2}; (2, \frac{1}{2})$