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