Chapter 4: Q 4.101 (page 456)

Solve the system of equations using Cramer’s rule:

$\{\begin{cases} 4 x - 3 y = 8 \\ 8 x - 3 y = 14 \end{cases}$

Short Answer

Expert verified

The system is inconsistent. So, There is no solution.

Step by step solution

Step 1. Given information

The given linear equations are

$\{\begin{cases} 4 x - 3 y = 8 \\ 8 x - 3 y = 14 \end{cases}$

Step 2. Evaluate the determinant D, using the coefficients of the variables

$D = [\begin{matrix} 4 & - 3 \\ 8 & - 6 \end{matrix}] D = (4 \times - 6) - (- 3 \times 8) D = - 24 + 24 D = 0$

We cannot use Cramer’s Rule to solve this system. But by looking at the value of the determinants D_x and D_y, we can determine whether the system is dependent or inconsistent.

Step 3. Evaluate the determinant Dx and Dy.

$D_{x} = [\begin{matrix} 8 & - 3 \\ 14 & - 6 \end{matrix}] D_{x} = (8 \times - 6) - (- 3 \times 14) D_{x} = - 48 + 42 D_{x} = - 6 D_{y} = [\begin{matrix} 4 & 8 \\ 8 & 14 \end{matrix}] D_{y} = (4 \times 14) - (8 \times 8) D_{y} = 56 - 64 D_{y} = - 8 Since all the determinants are not zero, the system is inconsistent . There is no solution .$

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Solve the system of equations using Cramer’s rule:

$\{\begin{cases} 4 x - 3 y = 8 \\ 8 x - 3 y = 14 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluate the determinant D, using the coefficients of the variables

Step 3. Evaluate the determinant Dx and Dy.

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Solve the system of equations using Cramer’s rule:4x-3y=88x-3y=14

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluate the determinant D, using the coefficients of the variables

Step 3. Evaluate the determinant Dx and Dy.

One App. One Place for Learning.

Most popular questions from this chapter

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Logic and Functions

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Study anywhere. Anytime. Across all devices.

Solve the system of equations using Cramer’s rule:

$\{\begin{cases} 4 x - 3 y = 8 \\ 8 x - 3 y = 14 \end{cases}$