Chapter 11: Q. 15 (page 740)

Solve the system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.
$\{\begin{cases} x + y = 8 \\ x - y = 4 \end{cases}$

Short Answer

Expert verified

$x = 6 y = 2$

Step by step solution

Step 1. Given information

We have been given a system of equations:

$\{\begin{cases} x + y = 8 \\ x - y = 4 \end{cases}$

We have to solve this system of equations using Cramer’s Rule if it is applicable.

Step 2. Check determinant

$|\begin{matrix} 1 & 1 \\ 1 & - 1 \end{matrix}| = 1 \times (- 1) - 1 \times 1 = - 1 - 1 = - 2$

Since the determinant is non zero, so Cramer's rule is applicable.

Step 3. Use Cramer's rule

Find $D_{x}$ and $D_{y}$ .

$D_{x} = |\begin{matrix} 8 & 1 \\ 4 & - 1 \end{matrix}| = 8 \times (- 1) - 4 \times 1 = - 8 - 4 = - 12$

$D_{y} = |\begin{matrix} 1 & 8 \\ 1 & 4 \end{matrix}| = 1 \times 4 - 1 \times 8 = 4 - 8 = - 4$

Step 4. Find x and y

$x = \frac{D_{x}}{D} = \frac{- 12}{- 2} = 6 y = \frac{D_{y}}{D} = \frac{- 4}{- 2} = 2$

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Solve the system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.
$\{\begin{cases} x + y = 8 \\ x - y = 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Check determinant

Step 3. Use Cramer's rule

Step 4. Find x and y

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Solve the system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.x+y=8x-y=4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Check determinant

Step 3. Use Cramer's rule

Step 4. Find x and y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve the system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.
$\{\begin{cases} x + y = 8 \\ x - y = 4 \end{cases}$