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Chapter 11: Q. 17 (page 740)

In Problems 15 鈥� 42, solve each system of equations using Cramer鈥檚 Rule if it is applicable. If Cramer鈥檚 Rule is not applicable, say so.

5x-y=132x+3y=12

Short Answer

Expert verified

The solution isx=3,y=2andinorderedpairis3,2.

Step by step solution

01

Step 1. Given Information 

The given system of equation is

5x-y=132x+3y=12

We have to solve the system of equations using Cramer's rule if it is applicable.

02

Step 2. Finding the determinant 

The determinantD of the coefficients of the variables is

D=5-123D=53--12D=15--2D=17

SinceD鈮�0 Cramer's rule is applicable.

03

Step 3. Use Cramer's rule 

Let's findDxandDy

localid="1647428335291" Dx=13-1123Dx=133--112Dx=39+12Dx=51

And

localid="1647428350891" Dy=513212Dy=512-132Dy=60-26Dy=34

04

Step 4. Finding x and y 

By using Cramer's rule, the values of xand yare

x=DxDandy=DyDx=5117andy=3417x=3andy=2

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