Problem to solve
Solve \[3x+5y=2\], \[-5x+6y=5\]
Solution
STEP 1
Solve the following system:
{5 y + 3 x = 2
6 y - 5 x = 5
STEP 2
Express the system in matrix form:
(3 | 5
-5 | 6)(x
y) = (2
5)
STEP 3
Write the system in augmented matrix form and use Gaussian elimination:
(3 | 5 | 2
-5 | 6 | 5)
STEP 4
Swap row 1 with row 2:
(-5 | 6 | 5
3 | 5 | 2)
STEP 5
Add 3/5 × (row 1) to row 2:
(-5 | 6 | 5
0 | 43/5 | 5)
STEP 6
Multiply row 2 by 5:
(-5 | 6 | 5
0 | 43 | 25)
STEP 7
Divide row 2 by 43:
(-5 | 6 | 5
0 | 1 | 25/43)
STEP 8
Subtract 6 × (row 2) from row 1:
(-5 | 0 | 65/43
0 | 1 | 25/43)
STEP 9
Divide row 1 by -5:
(1 | 0 | -13/43
0 | 1 | 25/43)
STEP 10
Collect results:
Answer: | 
 | {x = -13/43
y = 25/43