Problem to solve
Solve \[3y+5x+1-2y=2y-3\], \[3y-2+5x=2x-3y+2\]
Solution
STEP 1
Solve the following system:
{y + 5 x + 1 = 2 y - 3
3 y + 5 x - 2 = -3 y + 2 x + 2
STEP 2
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{y + 5 x + 1 = 2 y - 3
3 y + 5 x - 2 = -3 y + 2 x + 2
STEP 3
Hint: | Isolate terms with x to the left hand side.
Subtract y + 1 from both sides:
{5 x = y - 4
3 y + 5 x - 2 = -3 y + 2 x + 2
STEP 4
Hint: | Solve for x.
Divide both sides by 5:
{x = y/5 - 4/5
3 y + 5 x - 2 = -3 y + 2 x + 2
STEP 5
Hint: | Perform a substitution.
Substitute x = y/5 - 4/5 into the second equation:
{x = y/5 - 4/5
-2 + 5 (y/5 - 4/5) + 3 y = 2 + 2 (y/5 - 4/5) - 3 y
STEP 6
Hint: | Expand the left hand side of the equation -2 + 5 (y/5 - 4/5) + 3 y = 2 + 2 (y/5 - 4/5) - 3 y.
-2 + 5 (y/5 - 4/5) + 3 y = 3 y + (y - 4) - 2 = 4 y - 6:
{x = y/5 - 4/5
(4 y - 6) = 2 + 2 (y/5 - 4/5) - 3 y
STEP 7
Hint: | Expand the right hand side of the equation 4 y - 6 = 2 + 2 (y/5 - 4/5) - 3 y.
2 + 2 (y/5 - 4/5) - 3 y = -3 y + ((2 y)/5 - 8/5) + 2 = -(13 y)/5 + 2/5:
{x = y/5 - 4/5
4 y - 6 = (-(13 y)/5 + 2/5)
STEP 8
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = y/5 - 4/5
4 y - 6 = -(13 y)/5 + 2/5
STEP 9
Hint: | Isolate y to the left hand side.
Add (13 y)/5 + 6 to both sides:
{x = y/5 - 4/5
(33 y)/5 = 32/5
STEP 10
Hint: | Solve for y.
Multiply both sides by 5/33:
{x = y/5 - 4/5
y = 32/33
STEP 11
Hint: | Perform a back substitution.
Substitute y = 32/33 into the first equation:
Answer: | 
 | {x = -20/33
y = 32/33