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