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Chapter 4: Q 4.98 (page 453)

Solve using Cramer's rule

-x+y=22x+y=-4

Short Answer

Expert verified

The value of x=-2y=0

Step by step solution

01

Step 1. Given information

The given equations are -x+y=22x+y=-4

02

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

D=-1121=-1脳1-1脳2=-1-2=-3

03

Step 3.Evaluate the determinant Dx and Dy.

Fore the determinant of Dx ,

we replace the coefficients of x , -1 and 2 with the constants, 2 and -4.

Dx=21-41=2脳1-1脳-4=2+4=6

Fore the determinant of Dy ,

we replace the coefficients of y , 1 and 1 with the constants, 2 and -4.

Dy=-122-4=-1脳-4-2脳2=4-4=0

04

Step 4. Find x and y. 

x=DxDandy=DyDx=6-3andy=0-3Theorderedpairis(-2,0).

Substitute the values in the linear equation.

As the points satisfy the equations, Hence(-2,0). it is the solution to the system

05

Step 5.  Checking the values

Substitute the value
x=-2,y=0

intheequation-x+y=2-(-2)+0=22=2Alsosubstitutethevaluex=-2,y=0intheequation2x+y=-42(-2)+0=-4-4=-4True

Hence the solution to the equation is

x=-2,y=0

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