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Chapter 4: Q 267 (page 459)

Use Cramer鈥檚 Rule to Solve Systems of Equations

In the following exercises, solve each system of equations using Cramer鈥檚 Rule.

4x+3y=220x+15y=5

Short Answer

Expert verified

The system is inconsistent and it has no solution.

Step by step solution

01

Given system of equations are,

4x+3y=220x+15y=5

The objective is, we need to solve the given system of equations by using the Cramer's rule.

02

Step 2 Find the determinant D by using the coefficients of the variables.

D=432015=60-60=0

Here we cannot use Cramer's rule to solve this system. But by looking at the value of the determinants Dx,Dy, we can determine whether the system is dependent or inconsistent.

03

Step 3 Evaluate the determinant Dx by using the constants to replace the coefficients of x.

Dx=23515=215-35=30-15=15

04

Step 4 Evaluate the determinant Dy by using the constants to replace the coefficients of y.

Dy=42205=45-220=20-40=-20

Here all the determinants are not equal to zero.

So, the system is inconsistent and it has no solution.

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