Cramer's Rule Method calculator

SolutionHelp

Solve linear equation in two variables

1. 12x + 5y = 7 and 2x + 3y - 5 = 0

2. x + y = 2 and 2x + 3y = 4

3. 7y + 2x - 11 = 0 and 3x - y - 5 = 0

4. 3x - y - 5 = 0 and 2x + 7y - 11 = 0

5. 3x - y = 3 and 7x + 2y = 20

6. 2x - y = 11 and 5x + 4y = 1

7. 2x - 7y = 1 and 4x + 3y = 15

8. 3x - 5y = 1 and 5x + 2y = 19

9. 5x + 8y = 9 and 3y + 2x = 4

10. - 6x + 5y = 2 and - 5x + 6y = 9

11. 7x - 8y - 11 = 0 and 8x - 7y - 7 = 0

Example

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.

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

$D_x$

	$1$	$-2$
	$3$	$-4$

$=1 × (-4) - (-2) × 3$

$=-4 +6$

$=2$

$D_y$

	$1$	$-2$
	$2$	$-4$

$=1 × (-4) - (-2) × 2$

$=-4 +4$

$=0$

$D$

	$1$	$1$
	$2$	$3$

$=1 × 3 - 1 × 2$

$=3 -2$

$=1$

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

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

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

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

$:.x=2,y=0$