using cramer's rule solve the following system?

Question

2x-9y=5
3x-3y=11

Answer 1

x = det[[5 -9], [11, -3]] / det[[2 -9], [3 -3]]
y = det[[2 5], [3, 11]] / det[[2 -9], [3 -3]]

Answer 2

Cramer's Rule uses matrices to solve systems. Specifically, you set up three matrices, find their determinants, and divide them in specified ways to get the solutions.

The first matrix is coefficient matrix, containing just the coefficients of the variables. It is
[ 2 -9 ]
[ 3 -3 ]
To get the determinant multiply top left times bottom right and subtract top right times bottom left
D = 2 * (-3) - (-9) * 3 = -6+27=21

Next create a matrix where you substitute the numbers on the right side of the system for the x-column of your original matrix
[ 5 -9 ]
[ 11 -3 ]
Take its determinant: Dx = 5 * (-3) - (-9) * 11 = 84
The value for x is Dx / D = 84/21 = 4

Finally, make a third matrix replacing y-column in your orignal matrix with the numbers on the right.
[ 2 5 ]
[ 3 11]
Find its determinant Dy = 7
The value for y is Dy / D = 7/21 = 1/3

You can check by plugging the values back into the system. Cramer's rule is valuable because it works for systems of any size. Good luck.

Answer 3

2..-9|5
3..-3|11

x = N1/D and y = N2/D

D = 2*-3 - (-9)*3 = -6 + 27 = 21

.........5...-9
N1 =11..-3 = 5*-3 -(-9)*11 = -15 + 99 = 84; so that x = N1/D = 84/21 = 4

You can now do N2/D in the same way to find y OR do it the smart way and simply plug in x = 4 in the first equation. 2x - 9y = 5 = 8 - 9y = 5; so that 3 = 9y and y = 1/3.