First we need to transform the equations into standard form (Ax + By = C). the first equation is already in standard form. Adding 3x to each side of the second equation we get:
-6x+2y = 2
3x+ y = 1
By Cramer's Rule (Note: one "m"):
| 2 2 |
| 1 1 |
x = ---------
| -6 2 |
| 3 1 |
(Note: The denominator is the determinant of the coefficients of the x's and y's. The numerator is the same as the denominator except the "x column" has been replaced with the C's from the equations.)
2*1 - 2*1
x = ------------
-6*1 - 2*3
2 - 2
x = ------------
-6 - 6
0
x = ------------
-12
x = 0
Repeating for y:
| -6 2 |
| 3 1 |
y = ---------
| -6 2 |
| 3 1 |
(Note: The numerator is the same as the denominator except the "y column" has been replaced with the C's from the equations.)
-6*1 - 2*3
y = ------------
-6*1 - 2*3
-6 - 6
y = -------------
-6 - 6
-12
y = -----
-12
y = 1