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
Hint: | Expand the left hand side of the equation 1/2 (-y + 2 x) - 2/5 (-y + x) = -1.
(-y + 2 x)/2 - (2 (-y + x))/5 = ((2 y)/5 - (2 x)/5) + (-y/2 + x) = -y/10 + (3 x)/5:
{(-y/10 + (3 x)/5) = -1
4 (2 x + 3) + 1/2 (4 y - 3 x) = 5
STEP 3
Hint: | Expand the left hand side of the equation 4 (2 x + 3) + 1/2 (4 y - 3 x) = 5.
4 (2 x + 3) + (4 y - 3 x)/2 = (8 x + 12) + (2 y - (3 x)/2) = 2 y + (13 x)/2 + 12:
{-y/10 + (3 x)/5 = -1
(2 y + (13 x)/2 + 12) = 5
STEP 4
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{-y/10 + (3 x)/5 = -1
2 y + (13 x)/2 + 12 = 5
STEP 5
Hint: | Isolate terms with x to the left hand side.
Add y/10 to both sides:
{(3 x)/5 = (y - 10)/10
2 y + (13 x)/2 + 12 = 5
STEP 6
Hint: | Solve for x.
Multiply both sides by 5/3:
{x = (y - 10)/6
2 y + (13 x)/2 + 12 = 5
STEP 7
Hint: | Perform a substitution.
Substitute x = (y - 10)/6 into the second equation:
{x = (y - 10)/6
12 + (13 (y - 10))/12 + 2 y = 5
STEP 8
Hint: | Expand the left hand side of the equation 12 + (13 (y - 10))/12 + 2 y = 5.
12 + (13 (y - 10))/12 + 2 y = ((13 y)/12 - 65/6) + 2 y + 12 = (37 y)/12 + 7/6:
{x = (y - 10)/6
((37 y)/12 + 7/6) = 5
STEP 9
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = (y - 10)/6
(37 y)/12 + 7/6 = 5
STEP 10
Hint: | Isolate terms with y to the left hand side.
Subtract 7/6 from both sides:
{x = (y - 10)/6
(37 y)/12 = 23/6
STEP 11
Hint: | Solve for y.
Multiply both sides by 12/37:
{x = (y - 10)/6
y = 46/37
STEP 12
Hint: | Perform a back substitution.
Substitute y = 46/37 into the first equation:
Answer: | 
 | {x = -54/37
y = 46/37