Question 47337
-2x + 3y = 16
4x = -3y + 40


becomes
-2x + 3y = 16
4x + 3y = 40


in matrix form, we have:


{{{ matrix(2,2,
-2, 3,
4, 3) }}}


And its determinant is (-2)(3) - (4)(3)
D = -6 - 12
D = -18


Now re-write the matrix as: {{{ matrix(2,2,
16, 3,
40, 3) }}}


to calculate the x-version Determinant, Dx --> (16)(3) - (40)(3)
Dx = 48 - 120
Dx = - 72


Now re-write the matrix as: {{{ matrix(2,2,
-2, 16,
4, 40) }}}


to calculate the y-version Determinant, Dy --> (-2)(40) - (16)(4)
Dy = -80 - 64
Dy = -144


Now, x = Dx/D
x = -72/-18
x = 4

and y = Dy/D
y = -144/-18
y = 8


check:
-2x + 3y = 16
-2(4) + 3(8)
-8 + 24
16 --> correct


4x + 3y = 40
4(4) + 3(8)
16 + 24
40 --> correct


Look at my Lesson on a 3x3 Matrix using Cramer's Rule


jon.