Problem to solve
Solve \[\frac{x+2}{2}+\frac{3y-1}{4}=-1\], \[2x+y-2[3x-4y]=x+3\]
Solution
STEP 1
Solve the following system:
{(x + 2)/2 + 1/4 (3 y - 1) = -1
2 x - 2 (-4 y + 3 x) + y = x + 3
STEP 2
Hint: | Expand the left hand side of the equation (x + 2)/2 + 1/4 (3 y - 1) = -1.
(x + 2)/2 + (3 y - 1)/4 = (x/2 + 1) + ((3 y)/4 - 1/4) = (3 y)/4 + x/2 + 3/4:
{((3 y)/4 + x/2 + 3/4) = -1
2 x - 2 (-4 y + 3 x) + y = x + 3
STEP 3
Hint: | Expand the left hand side of the equation 2 x - 2 (-4 y + 3 x) + y = x + 3.
2 x - 2 (-4 y + 3 x) + y = 2 x + (8 y - 6 x) + y = 9 y - 4 x:
{(3 y)/4 + x/2 + 3/4 = -1
(9 y - 4 x) = x + 3
STEP 4
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{(3 y)/4 + x/2 + 3/4 = -1
9 y - 4 x = x + 3
STEP 5
Hint: | Isolate terms with x to the left hand side.
Subtract (3 y)/4 + 3/4 from both sides:
{x/2 = -(3 y)/4 - 7/4
9 y - 4 x = x + 3
STEP 6
Hint: | Solve for x.
Multiply both sides by 2:
{x = -(3 y)/2 - 7/2
9 y - 4 x = x + 3
STEP 7
Hint: | Perform a substitution.
Substitute x = -(3 y)/2 - 7/2 into the second equation:
{x = -(3 y)/2 - 7/2
9 y - 4 (-(3 y)/2 - 7/2) = -(3 y)/2 - 1/2
STEP 8
Hint: | Expand the left hand side of the equation 9 y - 4 (-(3 y)/2 - 7/2) = -(3 y)/2 - 1/2.
9 y - 4 (-(3 y)/2 - 7/2) = (6 y + 14) + 9 y = 15 y + 14:
{x = -(3 y)/2 - 7/2
(15 y + 14) = -(3 y)/2 - 1/2
STEP 9
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = -(3 y)/2 - 7/2
15 y + 14 = -(3 y)/2 - 1/2
STEP 10
Hint: | Isolate y to the left hand side.
Subtract -(3 y)/2 + 14 from both sides:
{x = -(3 y)/2 - 7/2
(33 y)/2 = -29/2
STEP 11
Hint: | Solve for y.
Multiply both sides by 2/33:
{x = -(3 y)/2 - 7/2
y = -29/33
STEP 12
Hint: | Perform a back substitution.
Substitute y = -29/33 into the first equation:
Answer: | 
 | {x = -24/11
y = -29/33