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