Chapter 11: Q. 46 (page 729)

In Problems 37–72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x - y = - 1 \\ x + \frac{1}{2} y = \frac{3}{2} \end{cases}$

Short Answer

Expert verified

The solution of the system is $x = \frac{1}{2}, y = 2$ ,or, using ordered pair, $(\frac{1}{2}, 2)$ .

Step by step solution

Step 1. Given information.

The given system of equation are

$\{\begin{cases} 2 x - y = - 1 \\ x + \frac{1}{2} y = \frac{3}{2} \end{cases}$

Step 2. Calculation.

The augmented matrix of the system is:

$[\begin{matrix} \begin{matrix} 2 & - 1 \\ 1 & \frac{1}{2} \end{matrix} & \begin{matrix} - 1 \\ \frac{3}{2} \end{matrix} \end{matrix}]$

Perform the row operations $R_{2} = 2 r_{2} - r_{1}$ :

$[\begin{matrix} \begin{matrix} 2 & - 1 \\ 0 & 2 \end{matrix} & \begin{matrix} - 1 \\ 4 \end{matrix} \end{matrix}]$

Perform the row operations $R_{2} = \frac{1}{2} r_{2}$ :

$[\begin{matrix} \begin{matrix} 2 & - 1 \\ 0 & 1 \end{matrix} & \begin{matrix} - 1 \\ 2 \end{matrix} \end{matrix}]$

Use the obtained matrix to write the system of equations.

$2 x - y = - 1 y = 2$

Step 3. Solve the equation.

Solve the equations to find the solution set.

Substitute $y = 2$ into the equation.

$2 x - y = - 1 2 x - 2 = - 1 2 x = - 1 + 2 2 x = 1 x = \frac{1}{2}$

Therefore, the solution of the system is $x = \frac{1}{2}, y = 2$ or, using ordered pair, $(\frac{1}{2}, 2)$ .

Step 4. Conclusion.

The solution of the system is $x = \frac{1}{2}, y = 2$ or, using ordered pair, $(\frac{1}{2}, 2)$ .

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In Problems 37–72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x - y = - 1 \\ x + \frac{1}{2} y = \frac{3}{2} \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Solve the equation.

Step 4. Conclusion.

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In Problems 37–72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.2x-y=-1x+12y=32

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Solve the equation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 37–72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x - y = - 1 \\ x + \frac{1}{2} y = \frac{3}{2} \end{cases}$