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Chapter 4: Q 4.101 (page 456)

Solve the system of equations using Cramer鈥檚 rule:


4x-3y=88x-3y=14

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information

The given linear equations are

4x-3y=88x-3y=14

02

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

D=4-38-6D=(4脳-6)-(-3脳8)D=-24+24D=0

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

03

Step 3. Evaluate the determinant Dx and Dy. 

Dx=8-314-6Dx=(8脳-6)-(-3脳14)Dx=-48+42Dx=-6Dy=48814Dy=(4脳14)-(8脳8)Dy=56-64Dy=-8Sinceallthedeterminantsarenotzero,thesystemisinconsistent.Thereisnosolution.

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