Problem to solve
Solve \[\frac{2x+y}{3}-\frac{2[x+y]}{4}=2\], \[-\frac{2[x-y]}{5}-\frac{x+2y}{2}=-1\]
Solution
STEP 1
Solve the following system:
{1/2 (-y - x) + 1/3 (y + 2 x) = 2 | (equation 1)
1/2 (-2 y - x) - 2/5 (-y + x) = -1 | (equation 2)
STEP 2
Express the system in standard form:
{x/6 - y/6 = 2 | (equation 1)
-(9 x)/10 - (3 y)/5 = -1 | (equation 2)
STEP 3
Swap equation 1 with equation 2:
{-(9 x)/10 - (3 y)/5 = -1 | (equation 1)
x/6 - y/6 = 2 | (equation 2)
STEP 4
Add 5/27 × (equation 1) to equation 2:
{-(9 x)/10 - (3 y)/5 = -1 | (equation 1)
0 x - (5 y)/18 = 49/27 | (equation 2)
STEP 5
Multiply equation 1 by -10:
{9 x + 6 y = 10 | (equation 1)
0 x - (5 y)/18 = 49/27 | (equation 2)
STEP 6
Multiply equation 2 by 54:
{9 x + 6 y = 10 | (equation 1)
0 x - 15 y = 98 | (equation 2)
STEP 7
Divide equation 2 by -15:
{9 x + 6 y = 10 | (equation 1)
0 x+y = -98/15 | (equation 2)
STEP 8
Subtract 6 × (equation 2) from equation 1:
{9 x+0 y = 246/5 | (equation 1)
0 x+y = -98/15 | (equation 2)
STEP 9
Divide equation 1 by 9:
{x+0 y = 82/15 | (equation 1)
0 x+y = -98/15 | (equation 2)
STEP 10
Collect results:
Answer: | 
 | {x = 82/15
y = -98/15