Problem to solve
Solve \[ 4x-5y=3\], \[-2x+6y=-2\]
Solution
STEP 1
Solve the following system:
{-5 y + 4 x = 3
6 y - 2 x = -2
STEP 2
Express the system in matrix form:
(4 | -5
-2 | 6)(x
y) = (3
-2)
STEP 3
Write the system in augmented matrix form and use Gaussian elimination:
(4 | -5 | 3
-2 | 6 | -2)
STEP 4
Add 1/2 × (row 1) to row 2:
(4 | -5 | 3
0 | 7/2 | -1/2)
STEP 5
Multiply row 2 by 2:
(4 | -5 | 3
0 | 7 | -1)
STEP 6
Divide row 2 by 7:
(4 | -5 | 3
0 | 1 | -1/7)
STEP 7
Add 5 × (row 2) to row 1:
(4 | 0 | 16/7
0 | 1 | -1/7)
STEP 8
Divide row 1 by 4:
(1 | 0 | 4/7
0 | 1 | -1/7)
STEP 9
Collect results:
Answer: | 
 | {x = 4/7
y = -1/7