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Chapter 4: Q 4.102 (page 456)

Solve the system of equations using Cramer鈥檚 rule:x+3y=42x+6y=8

Short Answer

Expert verified

Here, all the determinants are equal to zero.

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

Step by step solution

01

Step 1. Given information

The given linear equations are

x+3y=42x+6y=8

02

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

D=1326D=1脳6-3脳2D=6-6D=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.  

Dx=4386Dx=4脳6-3脳8Dx=24-24Dx=0Here,allthedeterminantsareequaltozero.So,thesystemisconsistentanddependentandithasinfinitelymanysolutions.

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