Problem to solve
Solve \[3y+5x+1-2y=2y-3\], \[3y-2+5x=2x-3y+2\]
Solution
STEP 1
Solve the following system:
{y + 5 x + 1 = 2 y - 3
3 y + 5 x - 2 = -3 y + 2 x + 2
STEP 2
Express the system in standard form:
{5 x - y = -4
3 x + 6 y = 4
STEP 3
Express the system in matrix form:
(5 | -1
3 | 6)(x
y) = (-4
4)
STEP 4
Write the system in augmented matrix form and use Gaussian elimination:
(5 | -1 | -4
3 | 6 | 4)
STEP 5
Subtract 3/5 × (row 1) from row 2:
(5 | -1 | -4
0 | 33/5 | 32/5)
STEP 6
Multiply row 2 by 5:
(5 | -1 | -4
0 | 33 | 32)
STEP 7
Divide row 2 by 33:
(5 | -1 | -4
0 | 1 | 32/33)
STEP 8
Add row 2 to row 1:
(5 | 0 | -100/33
0 | 1 | 32/33)
STEP 9
Divide row 1 by 5:
(1 | 0 | -20/33
0 | 1 | 32/33)
STEP 10
Collect results:
Answer: | 
 | {x = -20/33
y = 32/33