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