Problem to solve
Solve \[-2x+6y-4x=5x-3y+3\], \[7y+4x=9-2y\]
Solution
STEP 1
Solve the following system:
{6 y - 6 x = -3 y + 5 x + 3
7 y + 4 x = -2 y + 9
STEP 2
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{6 y - 6 x = -3 y + 5 x + 3
7 y + 4 x = -2 y + 9
STEP 3
Hint: | Isolate terms with x to the left hand side.
Subtract 7 y from both sides:
{6 y - 6 x = -3 y + 5 x + 3
4 x = -9 y + 9
STEP 4
Hint: | Solve for x.
Divide both sides by 4:
{6 y - 6 x = -3 y + 5 x + 3
x = -(9 y)/4 + 9/4
STEP 5
Hint: | Perform a substitution.
Substitute x = -(9 y)/4 + 9/4 into the first equation:
{6 y - 6 (-(9 y)/4 + 9/4) = 3 + 5 (-(9 y)/4 + 9/4) - 3 y
x = -(9 y)/4 + 9/4
STEP 6
Hint: | Expand the left hand side of the equation 6 y - 6 (-(9 y)/4 + 9/4) = 3 + 5 (-(9 y)/4 + 9/4) - 3 y.
6 y - 6 (-(9 y)/4 + 9/4) = ((27 y)/2 - 27/2) + 6 y = (39 y)/2 - 27/2:
{((39 y)/2 - 27/2) = 3 + 5 (-(9 y)/4 + 9/4) - 3 y
x = -(9 y)/4 + 9/4
STEP 7
Hint: | Expand the right hand side of the equation (39 y)/2 - 27/2 = 3 + 5 (-(9 y)/4 + 9/4) - 3 y.
3 + 5 (-(9 y)/4 + 9/4) - 3 y = -3 y + (-(45 y)/4 + 45/4) + 3 = -(57 y)/4 + 57/4:
{(39 y)/2 - 27/2 = (-(57 y)/4 + 57/4)
x = -(9 y)/4 + 9/4
STEP 8
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for y:
{(39 y)/2 - 27/2 = -(57 y)/4 + 57/4
x = -(9 y)/4 + 9/4
STEP 9
Hint: | Isolate y to the left hand side.
Add (57 y)/4 + 27/2 to both sides:
{(135 y)/4 = 111/4
x = -(9 y)/4 + 9/4
STEP 10
Hint: | Solve for y.
Multiply both sides by 4/135:
{y = 37/45
x = -(9 y)/4 + 9/4
STEP 11
Hint: | Perform a back substitution.
Substitute y = 37/45 into the second equation:
{y = 37/45
x = 2/5
STEP 12
Hint: | Sort results.
Collect results in alphabetical order:
Answer: | 
 | {x = 2/5
y = 37/45