Problem to solve
Solve \[3x+2y=5\], \[-4x+5y=2\]
Solution
STEP 1
Solve the following system:
{2 y + 3 x = 5
5 y - 4 x = 2
STEP 2
Express the system in matrix form:
(3 | 2
-4 | 5)(x
y) = (5
2)
STEP 3
Write the system in augmented matrix form and use Gaussian elimination:
(3 | 2 | 5
-4 | 5 | 2)
STEP 4
Swap row 1 with row 2:
(-4 | 5 | 2
3 | 2 | 5)
STEP 5
Add 3/4 × (row 1) to row 2:
(-4 | 5 | 2
0 | 23/4 | 13/2)
STEP 6
Multiply row 2 by 4:
(-4 | 5 | 2
0 | 23 | 26)
STEP 7
Divide row 2 by 23:
(-4 | 5 | 2
0 | 1 | 26/23)
STEP 8
Subtract 5 × (row 2) from row 1:
(-4 | 0 | -84/23
0 | 1 | 26/23)
STEP 9
Divide row 1 by -4:
(1 | 0 | 21/23
0 | 1 | 26/23)
STEP 10
Collect results:
Answer: | 
 | {x = 21/23
y = 26/23