Chapter 11: Q. 52 (page 756)

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations.
$\{\begin{array}{l} b x + 3 y = 14 \\ b x + 2 y = 10 \end{array} b \neq 0$

Short Answer

Expert verified

The solution of the matrix is $x = \frac{2}{b} and y = 4$ .

Step by step solution

Step 1. Given Information

A matrix is given as,

$\{\begin{array}{l} b x + 3 y = 14 \\ b x + 2 y = 10 \end{array} b \neq 0$

We need to find the solution of the matrix using inverse of the matrix.

Step 2. Inverse of the matrix.

The inverse of the matrix is known as:

$A^{- 1} = [\begin{matrix} - \frac{2}{b} & \frac{3}{b} \\ 1 & - 1 \end{matrix}]$

Step 3. Solution of the matrix

We know,

$X = A^{- 1} B$

Therefore,

$X = [\begin{matrix} - \frac{2}{b} & \frac{3}{b} \\ 1 & - 1 \end{matrix}] [\begin{array}{l} 14 \\ 10 \end{array}] = [\begin{matrix} - \frac{2}{b} (14) + \frac{3}{b} (10) \\ 1 (14) - 1 (10) \end{matrix}] [\begin{array}{l} x \\ y \end{array}] = [\begin{array}{l} \frac{2}{b} \\ 4 \end{array}]$

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In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations.
$\{\begin{array}{l} b x + 3 y = 14 \\ b x + 2 y = 10 \end{array} b \neq 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Inverse of the matrix.

Step 3. Solution of the matrix

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In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations.bx+3y=14bx+2y=10b≠0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Inverse of the matrix.

Step 3. Solution of the matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Statistics

Decision Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations.
$\{\begin{array}{l} b x + 3 y = 14 \\ b x + 2 y = 10 \end{array} b \neq 0$