Chapter 11: Q. 20 (page 793)

In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 3 x - 2 y = 1 \\ 10 x + 10 y = 5 \end{array}$

Short Answer

Expert verified

The solution in ordered pair form is $(\frac{2}{5}, \frac{1}{10})$

Step by step solution

Step 1. Given information

The given system of equations is $\{\begin{array}{r} 3 x - 2 y = 1 \\ 10 x + 10 y = 5 \end{array}$

Step 2. Solve system of equations using matrix

Write the augmented matrix of the system,

$[\begin{array}{lll} 3 & - 2 & 1 \\ 2 & 2 & 1 \end{array}]$

Perform the operation $R_{1} = \frac{R_{1}}{3}$ ,

$[\begin{array}{lll} 3 & - 2 & 1 \\ 2 & 2 & 1 \end{array}] \to [\begin{array}{ccc} 1 & - \frac{2}{3} & \frac{1}{3} \\ 2 & 2 & 1 \end{array}]$

Now, perform the operation $R_{2} = R_{2} - 2 R_{1}$ ,

$[\begin{array}{ccc} 1 & - \frac{2}{3} & \frac{1}{3} \\ 2 & 2 & 1 \end{array}] \to [\begin{array}{ccc} 1 & - \frac{2}{3} & \frac{1}{3} \\ 0 & \frac{10}{3} & \frac{1}{3} \end{array}]$

Now, perform the operation $R_{2} = R_{2} \cdot \frac{3}{10}$ ,

$[\begin{array}{ccc} 1 & - \frac{2}{3} & \frac{1}{3} \\ 0 & \frac{10}{3} & \frac{1}{3} \end{array}] \to [\begin{array}{ccc} 1 & - \frac{2}{3} & \frac{1}{3} \\ 0 & 1 & \frac{1}{10} \end{array}]$

Now, write the system of equations for this obtained augmented matrix,

$\{\begin{cases} x - \frac{2}{3} y = \frac{1}{3} \\ y = \frac{1}{10} \end{cases}$

Now,

role="math" localid="1646998275861" $x - \frac{2}{3} \cdot \frac{1}{10} = \frac{1}{3} x = \frac{1}{3} + \frac{1}{15} x = \frac{2}{5}$

So, The solution in ordered pair form is $(\frac{2}{5}, \frac{1}{10})$

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In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 3 x - 2 y = 1 \\ 10 x + 10 y = 5 \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve system of equations using matrix

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In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.3x−2y=110x+10y=5

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve system of equations using matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Statistics

Calculus

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 3 x - 2 y = 1 \\ 10 x + 10 y = 5 \end{array}$