Chapter 4: Q9. (page 194)

Use Cramer’s rule to solve each system of equations.
9.
$\begin{matrix} 7 r + 5 s = 3 \\ 3 r - 2 s = 22 \end{matrix}$

Short Answer

Expert verified

The solution of the given system of equations is $(4, - 5)$ .

Step by step solution

- Description of step.

The solution of the system of linear equations in two variables:

$\begin{array}{l} a_{1} r + b_{1} s = c_{1} \\ a_{2} r + b_{2} s = c_{2} \end{array}$

by Cramer’s rule is given by $(r, s)$ where $r = \frac{| \begin{matrix} c_{1} & b_{1} \\ c_{2} & b_{2} \end{matrix} |}{| \begin{matrix} a_{1} & b_{1} \\ a_{2} & b_{2} \end{matrix} |}$ $s = \frac{| \begin{matrix} a_{1} & c_{1} \\ a_{2} & c_{2} \end{matrix} |}{| \begin{matrix} a_{1} & b_{1} \\ a_{2} & b_{2} \end{matrix} |}$ , and $| \begin{matrix} a_{1} & b_{1} \\ a_{2} & b_{2} \end{matrix} | \neq 0$ .

Step 2- Description of step.

The given system of linear equations in two variables is:

$\begin{array}{l} 7 r + 5 s = 3 \\ 3 r - 2 s = 22 \end{array}$

Therefore, by comparing the given system of linear equations with the system of linear .equations $\begin{array}{l} a_{1} r + b_{1} s = c_{1} \\ a_{2} r + b_{2} s = c_{2} \end{array}$ , it can be obtained that:

$a_{1} = 7$ , $b_{1} = 5$ , $c_{1} = 3$ , $a_{2} = 3$ , $b_{2} = - 2$ and $c_{2} = 22$ .

Step 3- Find the values of r and s.

The value of r is given by:

$\begin{matrix} r = \frac{| \begin{matrix} 3 & 5 \\ 22 & - 2 \end{matrix} |}{| \begin{matrix} 7 & 5 \\ 3 & - 2 \end{matrix} |} \\ = \frac{- 6 - (110)}{- 14 - (15)} \\ = \frac{- 6 - 110}{- 14 - 15} \\ = \frac{- 116}{- 29} \\ = 4 \end{matrix}$

The value of s is given by:

$\begin{matrix} s = \frac{| \begin{matrix} 7 & 3 \\ 3 & 22 \end{matrix} |}{| \begin{matrix} 7 & 5 \\ 3 & - 2 \end{matrix} |} \\ = \frac{154 - (9)}{- 14 - (15)} \\ = \frac{154 - 9}{- 14 - 15} \\ = \frac{145}{- 29} \\ = - 5 \end{matrix}$

The values of x and y are 4 and respectively.

Step 4- Description of step.

The solution of the given system of equations is $(4, - 5)$ .

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Use Cramer’s rule to solve each system of equations.
9.
$\begin{matrix} 7 r + 5 s = 3 \\ 3 r - 2 s = 22 \end{matrix}$

Short Answer

Step by step solution

- Description of step.

Step 2- Description of step.

Step 3- Find the values of r and s.

Step 4- Description of step.

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Use Cramer’s rule to solve each system of equations.9.7r+5s=33r-2s=22

Short Answer

Step by step solution

­- Description of step.

Step 2­- Description of step.

Step 3­- Find the values of r and s.

Step 4­- Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Decision Maths

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use Cramer’s rule to solve each system of equations.
9.
$\begin{matrix} 7 r + 5 s = 3 \\ 3 r - 2 s = 22 \end{matrix}$

- Description of step.

Step 2- Description of step.

Step 3- Find the values of r and s.

Step 4- Description of step.