Problem to solve
Solve \[\frac{x+2}{2}+\frac{3y-1}{4}=-1\], \[2x+y-2[3x-4y]=x+3\]
Solution
STEP 1
Solve the following system:
{(x + 2)/2 + 1/4 (3 y - 1) = -1
2 x - 2 (-4 y + 3 x) + y = x + 3
STEP 2
Express the system in standard form:
{x/2 + (3 y)/4 = -7/4
-5 x + 9 y = 3
STEP 3
Express the system in matrix form:
(1/2 | 3/4
-5 | 9)(x
y) = (-7/4
3)
STEP 4
Write the system in augmented matrix form and use Gaussian elimination:
(1/2 | 3/4 | -7/4
-5 | 9 | 3)
STEP 5
Swap row 1 with row 2:
(-5 | 9 | 3
1/2 | 3/4 | -7/4)
STEP 6
Add 1/10 × (row 1) to row 2:
(-5 | 9 | 3
0 | 33/20 | -29/20)
STEP 7
Multiply row 2 by 20:
(-5 | 9 | 3
0 | 33 | -29)
STEP 8
Divide row 2 by 33:
(-5 | 9 | 3
0 | 1 | -29/33)
STEP 9
Subtract 9 × (row 2) from row 1:
(-5 | 0 | 120/11
0 | 1 | -29/33)
STEP 10
Divide row 1 by -5:
(1 | 0 | -24/11
0 | 1 | -29/33)
STEP 11
Collect results:
Answer: | 
 | {x = -24/11
y = -29/33