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
4 (2 x + 3) + 1/2 (4 y - 3 x) = 5
STEP 2
Express the system in standard form:
{-y/10 + (3 x)/5 = -1
2 y + (13 x)/2 = -7
STEP 3
Express the system in matrix form:
(3/5 | -1/10
13/2 | 2)(x
y) = (-1
-7)
STEP 4
Solve the system with Cramer's rule:
x = (-1 | -1/10
-7 | 2)/(3/5 | -1/10
13/2 | 2) and y = (3/5 | -1
13/2 | -7)/(3/5 | -1/10
13/2 | 2)
STEP 5
Evaluate the determinant 3/5 | -1/10
13/2 | 2 = 37/20:
x = (-1 | -1/10
-7 | 2)/(37/20) and y = (3/5 | -1
13/2 | -7)/(37/20)
STEP 6
The gcd of -1 | -1/10
-7 | 2 and 37/20 is 1/20, so (-1 | -1/10
-7 | 2)/(37/20) = (20 -1 | -1/10
-7 | 2)/(20×37/20) = 20/37 -1 | -1/10
-7 | 2:
x = 20/37 -1 | -1/10
-7 | 2 and y = (3/5 | -1
13/2 | -7)/(37/20)
STEP 7
The gcd of 3/5 | -1
13/2 | -7 and 37/20 is 1/20, so (3/5 | -1
13/2 | -7)/(37/20) = (20 3/5 | -1
13/2 | -7)/(20×37/20) = 20/37 3/5 | -1
13/2 | -7:
x = (20 -1 | -1/10
-7 | 2)/37 and y = 20/37 3/5 | -1
13/2 | -7
STEP 8
Evaluate the determinant -1 | -1/10
-7 | 2 = (-27)/10:
x = 20/37×-27/10 and y = (20 3/5 | -1
13/2 | -7)/37
STEP 9
20/37×(-27)/10 = (-54)/37:
x = -54/37 and y = (20 3/5 | -1
13/2 | -7)/37
STEP 10
Evaluate the determinant 3/5 | -1
13/2 | -7 = 23/10:
x = (-54)/37 and y = 20/37×23/10
STEP 11
20/37×23/10 = 46/37:
Answer: | 
 | x = (-54)/37 and y = 46/37