Problem to solve
Solve \[-4x+5y+3=x+4\], \[6x-7y=2y-1\]
Solution
STEP 1
Solve the following system:
{5 y - 4 x + 3 = x + 4
-7 y + 6 x = 2 y - 1
STEP 2
Express the system in standard form:
{-5 x + 5 y = 1
6 x - 9 y = -1
STEP 3
Express the system in matrix form:
(-5 | 5
6 | -9)(x
y) = (1
-1)
STEP 4
Write the system in augmented matrix form and use Gaussian elimination:
(-5 | 5 | 1
6 | -9 | -1)
STEP 5
Swap row 1 with row 2:
(6 | -9 | -1
-5 | 5 | 1)
STEP 6
Add 5/6 × (row 1) to row 2:
(6 | -9 | -1
0 | -5/2 | 1/6)
STEP 7
Multiply row 2 by 6:
(6 | -9 | -1
0 | -15 | 1)
STEP 8
Divide row 2 by -15:
(6 | -9 | -1
0 | 1 | -1/15)
STEP 9
Add 9 × (row 2) to row 1:
(6 | 0 | -8/5
0 | 1 | -1/15)
STEP 10
Divide row 1 by 6:
(1 | 0 | -4/15
0 | 1 | -1/15)
STEP 11
Collect results:
Answer: | 
 | {x = -4/15
y = -1/15