Chapter 4: Q14. (page 192)

Use Cramer’s Rule to solve each system of equations.
$2 r - s = 1$
$3 r + 2 s = 19$

Short Answer

Expert verified

The required solution is $(3, 5)$ .

Step by step solution

Step 1- Determine the value of r

Apply the Cramer’s rule for the value of r.

$r = \frac{|\begin{matrix} e & b \\ f & d \end{matrix}|}{|\begin{matrix} a & b \\ c & d \end{matrix}|}$

Substitute 2 in place of a, 3 in place of c, $- 1$ in place of b, 2 in place of d, 1 in place of e and 19 in place of f into role="math" localid="1647189600339" $r = \frac{|\begin{matrix} e & b \\ f & d \end{matrix}|}{|\begin{matrix} a & b \\ c & d \end{matrix}|}$ and perform simplification of determinants to write the value of r.

$\begin{matrix} r = \frac{|\begin{matrix} 1 & - 1 \\ 19 & 2 \end{matrix}|}{|\begin{matrix} 2 & - 1 \\ 3 & 2 \end{matrix}|} \\ = \frac{1 \cdot 2 - (- 1) \cdot 19}{2 \cdot 2 - (- 1) \cdot 3} \\ = \frac{21}{7} \\ = 3 \end{matrix}$

– Determine the value of s

Apply the Cramer’s rule for the value of s.

$s = \frac{|\begin{matrix} a & e \\ c & f \end{matrix}|}{|\begin{matrix} a & b \\ c & d \end{matrix}|}$

Substitute 2 in place of a, 3 in place of c, $- 1$ in place of b, 2 in place of d, 1 in place of e and 19 in place of f into role="math" localid="1647189747064" $s = \frac{|\begin{matrix} a & e \\ c & f \end{matrix}|}{|\begin{matrix} a & b \\ c & d \end{matrix}|}$ and perform simplification of determinants to write the value of s.

$\begin{matrix} s = \frac{|\begin{matrix} 2 & 1 \\ 3 & 19 \end{matrix}|}{|\begin{matrix} 2 & - 1 \\ 3 & 2 \end{matrix}|} \\ = \frac{2 \cdot 19 - 1 \cdot 3}{2 \cdot 2 - (- 1) \cdot 3} \\ = \frac{35}{7} \\ = 5 \end{matrix}$

Step 3- Write the solution

The obtained value of r is 3 and s is 5 so the solution is $(3, 5)$ .

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Use Cramer’s Rule to solve each system of equations.
$2 r - s = 1$
$3 r + 2 s = 19$

Short Answer

Step by step solution

Step 1- Determine the value of r

– Determine the value of s

Step 3- Write the solution

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Use Cramer’s Rule to solve each system of equations.2r-s=13r+2s=19

Short Answer

Step by step solution

Step 1- Determine the value of r

– Determine the value of s

Step 3- Write the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Mechanics Maths

Calculus

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use Cramer’s Rule to solve each system of equations.
$2 r - s = 1$
$3 r + 2 s = 19$