Problem to solve
Solve \[-\frac{2[x-y]}{5}+\frac{2x-y}{2}=-1\], \[4[2x+3]-\frac{3x-4y}{2}=5\]
Solution
STEP 1
Solve the following system:
{1/2 (-y + 2 x) - 2/5 (-y + x) = -1 | (equation 1)
4 (2 x + 3) + 1/2 (4 y - 3 x) = 5 | (equation 2)
STEP 2
Express the system in standard form:
{(3 x)/5 - y/10 = -1 | (equation 1)
(13 x)/2 + 2 y = -7 | (equation 2)
STEP 3
Swap equation 1 with equation 2:
{(13 x)/2 + 2 y = -7 | (equation 1)
(3 x)/5 - y/10 = -1 | (equation 2)
STEP 4
Subtract 6/65 × (equation 1) from equation 2:
{(13 x)/2 + 2 y = -7 | (equation 1)
0 x - (37 y)/130 = -23/65 | (equation 2)
STEP 5
Multiply equation 1 by 2:
{13 x + 4 y = -14 | (equation 1)
0 x - (37 y)/130 = -23/65 | (equation 2)
STEP 6
Multiply equation 2 by -130:
{13 x + 4 y = -14 | (equation 1)
0 x+37 y = 46 | (equation 2)
STEP 7
Divide equation 2 by 37:
{13 x + 4 y = -14 | (equation 1)
0 x+y = 46/37 | (equation 2)
STEP 8
Subtract 4 × (equation 2) from equation 1:
{13 x+0 y = -702/37 | (equation 1)
0 x+y = 46/37 | (equation 2)
STEP 9
Divide equation 1 by 13:
{x+0 y = -54/37 | (equation 1)
0 x+y = 46/37 | (equation 2)
STEP 10
Collect results:
Answer: | 
 | {x = -54/37
y = 46/37