Problem to solve
Solve \[-2x+6y-4x=5x-3y+3\], \[7y+4x=9-2y\]
Solution
STEP 1
Solve the following system:
{6 y - 6 x = -3 y + 5 x + 3
7 y + 4 x = -2 y + 9
STEP 2
Express the system in standard form:
{-11 x + 9 y = 3
4 x + 9 y = 9
STEP 3
Express the system in matrix form:
(-11 | 9
4 | 9)(x
y) = (3
9)
STEP 4
Write the system in augmented matrix form and use Gaussian elimination:
(-11 | 9 | 3
4 | 9 | 9)
STEP 5
Add 4/11 × (row 1) to row 2:
(-11 | 9 | 3
0 | 135/11 | 111/11)
STEP 6
Multiply row 2 by 11/3:
(-11 | 9 | 3
0 | 45 | 37)
STEP 7
Divide row 2 by 45:
(-11 | 9 | 3
0 | 1 | 37/45)
STEP 8
Subtract 9 × (row 2) from row 1:
(-11 | 0 | -22/5
0 | 1 | 37/45)
STEP 9
Divide row 1 by -11:
(1 | 0 | 2/5
0 | 1 | 37/45)
STEP 10
Collect results:
Answer: | 
 | {x = 2/5
y = 37/45