Problem to solve
Solve \[\frac{3}{2}x-\frac{1}{2}y=6x-2\], \[3x+\frac{2}{3}y=-2y-1\]
Solution
STEP 1
Solve the following system:
{-y/2 + (3 x)/2 = 6 x - 2
(2 y)/3 + 3 x = -2 y - 1
STEP 2
Express the system in standard form:
{-(9 x)/2 - y/2 = -2
3 x + (8 y)/3 = -1
STEP 3
Express the system in matrix form:
(-9/2 | -1/2
3 | 8/3)(x
y) = (-2
-1)
STEP 4
Write the system in augmented matrix form and use Gaussian elimination:
(-9/2 | -1/2 | -2
3 | 8/3 | -1)
STEP 5
Add 2/3 × (row 1) to row 2:
(-9/2 | -1/2 | -2
0 | 7/3 | -7/3)
STEP 6
Multiply row 1 by -2:
(9 | 1 | 4
0 | 7/3 | -7/3)
STEP 7
Multiply row 2 by 3/7:
(9 | 1 | 4
0 | 1 | -1)
STEP 8
Subtract row 2 from row 1:
(9 | 0 | 5
0 | 1 | -1)
STEP 9
Divide row 1 by 9:
(1 | 0 | 5/9
0 | 1 | -1)
STEP 10
Collect results:
Answer: | 
 | {x = 5/9
y = -1