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Chapter 4: Q 265 (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.

x-4y=-1-3x+12y=3

Short Answer

Expert verified

The system is consistent and dependent and have infinitely many solutions.

Step by step solution

01

Given system of linear equations are,

x-4y=-1-3x+12y=3

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

02

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

D=1-4-312=112--4-3=12-12=0

We cannot solve this system by using the Cramer's rule. But by looking at the determinantsDx,Dy, we can determine whether the given system is dependent or inconsistent.

03

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

Dx=-1-4312=-112--43=-12+12=0

04

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

Dy=1-1-33=13--1-3=3-3=0

All the determinants are equal to zero.

So, the system is consistent and dependent and having infinitely many solutions.

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