Cramer's Rule Method Examples

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7. Cramer's Rule Method example ( Enter your problem )

( Enter your problem )

Examples

Other related methods

6. Inverse matrix method
(Previous method)

1. Examples

1. Solve linear equations x+y=2 and 2x+3y=4 using Cramer's Rule Method

Solution:
The equations can be expressed as
`x+y-2=0`

`2x+3y-4=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`D_x`

	`1`	`-2`
	`3`	`-4`

`=1 × (-4) - (-2) × 3`

`=-4 +6`

`=2`

`D_y`

	`1`	`-2`
	`2`	`-4`

`=1 × (-4) - (-2) × 2`

`=-4 +4`

`=0`

`D`

	`1`	`1`
	`2`	`3`

`=1 × 3 - 1 × 2`

`=3 -2`

`=1`

`(x)/D_x=(-y)/D_y=(1)/D`

`:.(x)/2=(-y)/0=(1)/1`

`:.(x)/2=(1)/1,(-y)/0=(1)/1`

`:.x=(2)/(1),y=(0)/(1)`

`:.x=2,y=0`

2. Solve linear equations 2x+7y-11=0 and 3x-y-5=0 using Cramer's Rule Method

Solution:
The equations can be expressed as
`2x+7y-11=0`

`3x-y-5=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`D_x`

	`7`	`-11`
	`-1`	`-5`

`=7 × (-5) - (-11) × (-1)`

`=-35 -11`

`=-46`

`D_y`

	`2`	`-11`
	`3`	`-5`

`=2 × (-5) - (-11) × 3`

`=-10 +33`

`=23`

`D`

	`2`	`7`
	`3`	`-1`

`=2 × (-1) - 7 × 3`

`=-2 -21`

`=-23`

`(x)/D_x=(-y)/D_y=(1)/D`

`:.(x)/-46=(-y)/23=(1)/-23`

`:.(x)/-46=(1)/-23,(-y)/23=(1)/-23`

`:.x=(-46)/(-23),y=(-23)/(-23)`

`:.x=2,y=1`

3. Solve linear equations 3x-y=3 and 7x+2y=20 using Cramer's Rule Method

Solution:
The equations can be expressed as
`3x-y-3=0`

`7x+2y-20=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`D_x`

	`-1`	`-3`
	`2`	`-20`

`=-1 × (-20) - (-3) × 2`

`=20 +6`

`=26`

`D_y`

	`3`	`-3`
	`7`	`-20`

`=3 × (-20) - (-3) × 7`

`=-60 +21`

`=-39`

`D`

	`3`	`-1`
	`7`	`2`

`=3 × 2 - (-1) × 7`

`=6 +7`

`=13`

`(x)/D_x=(-y)/D_y=(1)/D`

`:.(x)/26=(-y)/-39=(1)/13`

`:.(x)/26=(1)/13,(-y)/-39=(1)/13`

`:.x=(26)/(13),y=(39)/(13)`

`:.x=2,y=3`

4. Solve linear equations 2x-y=11 and 5x+4y=1 using Cramer's Rule Method

Solution:
The equations can be expressed as
`2x-y-11=0`

`5x+4y-1=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`D_x`

	`-1`	`-11`
	`4`	`-1`

`=-1 × (-1) - (-11) × 4`

`=1 +44`

`=45`

`D_y`

	`2`	`-11`
	`5`	`-1`

`=2 × (-1) - (-11) × 5`

`=-2 +55`

`=53`

`D`

	`2`	`-1`
	`5`	`4`

`=2 × 4 - (-1) × 5`

`=8 +5`

`=13`

`(x)/D_x=(-y)/D_y=(1)/D`

`:.(x)/45=(-y)/53=(1)/13`

`:.(x)/45=(1)/13,(-y)/53=(1)/13`

`:.x=(45)/(13),y=(-53)/(13)`

`:.x=45/13,y=-53/13`

This material is intended as a summary. Use your textbook for detail explanation.
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6. Inverse matrix method
(Previous method)

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