SOLUTION: 3x equals y plus 4 and x-y equals 6

Question 391137: 3x equals y plus 4 and x-y equals 6
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
Solve by graphing method:
3x=7+4_x-y=6
Add 4 to 7 to get 11.
3x=11_x-y=6
Divide each term in the equation by 3.
(3x)/(3)=(11)/(3)_x-y=6
Simplify the left-hand side of the equation by canceling the common factors.
x=(11)/(3)_x-y=6
Since x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting x from both sides.
x=(11)/(3)_-y=-x+6
Multiply each term in the equation by -1.
x=(11)/(3)_-y*-1=-x*-1+6*-1
Multiply -y by -1 to get y.
x=(11)/(3)_y=-x*-1+6*-1
Simplify the right-hand side of the equation by multiplying out all the terms.
x=(11)/(3)_y=x-6
Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.
x=(11)/(3)_y=x-6

Solving by Subtitution Method
3x=7+4_x-y=6
Add 4 to 7 to get 11.
3x=11_x-y=6
Divide each term in the equation by 3.
(3x)/(3)=(11)/(3)_x-y=6
Simplify the left-hand side of the equation by canceling the common factors.
x=(11)/(3)_x-y=6
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is (11)/(3).
x=(11)/(3)_((11)/(3))-y=6
Remove the parentheses around the expression (11)/(3).
x=(11)/(3)_(11)/(3)-y=6
Since (11)/(3) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (11)/(3) from both sides.
x=(11)/(3)_-y=-(11)/(3)+6
Simplify the right-hand side of the equation.
x=(11)/(3)_-y=(7)/(3)
Multiply each term in the equation by -1.
x=(11)/(3)_-y*-1=(7)/(3)*-1
Multiply -y by -1 to get y.
x=(11)/(3)_y=(7)/(3)*-1
Multiply (7)/(3) by -1 to get -(7)/(3).
x=(11)/(3)_y=-(7)/(3)
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is (11)/(3).
x=(11)/(3)_y=-(7)/(3)
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