Problem to solve
Solve \[3[x-5y]+2[2x-1]=2[x-y]\], \[2[x-1]-3[x-y]=-3x\]
Solution
STEP 1
Solve the following system:
{2 (2 x - 1) + 3 (-5 y + x) = 2 (-y + x)
2 (x - 1) - 3 (-y + x) = -3 x
STEP 2
Express the system in standard form:
{5 x - 13 y = 2
2 x + 3 y = 2
STEP 3
Express the system in matrix form:
(5 | -13
2 | 3)(x
y) = (2
2)
STEP 4
Write the system in augmented matrix form and use Gaussian elimination:
(5 | -13 | 2
2 | 3 | 2)
STEP 5
Subtract 2/5 × (row 1) from row 2:
(5 | -13 | 2
0 | 41/5 | 6/5)
STEP 6
Multiply row 2 by 5:
(5 | -13 | 2
0 | 41 | 6)
STEP 7
Divide row 2 by 41:
(5 | -13 | 2
0 | 1 | 6/41)
STEP 8
Add 13 × (row 2) to row 1:
(5 | 0 | 160/41
0 | 1 | 6/41)
STEP 9
Divide row 1 by 5:
(1 | 0 | 32/41
0 | 1 | 6/41)
STEP 10
Collect results:
Answer: | 
 | {x = 32/41
y = 6/41