Problem to solve
Solve \[\frac{2x-1}{4}+\frac{x-2y}{3}=4+x\], \[\frac{x+y}{3}-[x-y]=-2y+1\]
Solution
STEP 1
Solve the following system:
{1/4 (2 x - 1) + 1/3 (-2 y + x) = x + 4
-x + y + (y + x)/3 = -2 y + 1
STEP 2
Express the system in standard form:
{-(2 y)/3 - x/6 = 17/4
(10 y)/3 - (2 x)/3 = 1
STEP 3
Express the system in matrix form:
(-1/6 | -2/3
-2/3 | 10/3)(x
y) = (17/4
1)
STEP 4
Solve the system with Cramer's rule:
x = (17/4 | -2/3
1 | 10/3)/(-1/6 | -2/3
-2/3 | 10/3) and y = (-1/6 | 17/4
-2/3 | 1)/(-1/6 | -2/3
-2/3 | 10/3)
STEP 5
Evaluate the determinant -1/6 | -2/3
-2/3 | 10/3 = -1:
x = (17/4 | -2/3
1 | 10/3)/(-1) and y = (-1/6 | 17/4
-2/3 | 1)/(-1)
STEP 6
Simplify (17/4 | -2/3
1 | 10/3)/(-1):
x = -17/4 | -2/3
1 | 10/3 and y = (-1/6 | 17/4
-2/3 | 1)/(-1)
STEP 7
Simplify (-1/6 | 17/4
-2/3 | 1)/(-1):
x = -17/4 | -2/3
1 | 10/3 and y = --1/6 | 17/4
-2/3 | 1
STEP 8
Evaluate the determinant 17/4 | -2/3
1 | 10/3 = 89/6:
x = -89/6 and y = --1/6 | 17/4
-2/3 | 1
STEP 9
-89/6 = (-89)/6:
x = -89/6 and y = --1/6 | 17/4
-2/3 | 1
STEP 10
Evaluate the determinant -1/6 | 17/4
-2/3 | 1 = 8/3:
x = (-89)/6 and y = -8/3
STEP 11
-8/3 = (-8)/3:
Answer: | 
 | x = (-89)/6 and y = -8/3