Problem to solve
Solve \[3[x-5y]+2[2x-1]=2[x-y]\], \[2[x-1]-3[x-y]=-3x\]
Solution
STEP 1
Solve the following system:
{2 (2 x - 1) + 3 (-5 y + x) = 2 (-y + x) | (equation 1)
2 (x - 1) - 3 (-y + x) = -3 x | (equation 2)
STEP 2
Express the system in standard form:
{5 x - 13 y = 2 | (equation 1)
2 x + 3 y = 2 | (equation 2)
STEP 3
Subtract 2/5 × (equation 1) from equation 2:
{5 x - 13 y = 2 | (equation 1)
0 x+(41 y)/5 = 6/5 | (equation 2)
STEP 4
Multiply equation 2 by 5:
{5 x - 13 y = 2 | (equation 1)
0 x+41 y = 6 | (equation 2)
STEP 5
Divide equation 2 by 41:
{5 x - 13 y = 2 | (equation 1)
0 x+y = 6/41 | (equation 2)
STEP 6
Add 13 × (equation 2) to equation 1:
{5 x+0 y = 160/41 | (equation 1)
0 x+y = 6/41 | (equation 2)
STEP 7
Divide equation 1 by 5:
{x+0 y = 32/41 | (equation 1)
0 x+y = 6/41 | (equation 2)
STEP 8
Collect results:
Answer: | 
 | {x = 32/41
y = 6/41