Question 391189: x-y=1
x=1/2y+2
Found 2 solutions by haileytucki, Alan3354:
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! x-y=1_x=(1)/(2)*y+2
Multiply (1)/(2) by y to get (y)/(2).
x-y=1_x=(y)/(2)+2
Since -y does not contain the variable to solve for, move it to the right-hand side of the equation by adding y to both sides.
x=y+1_x=(y)/(2)+2
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is y+1.
x=y+1_(y+1)=(y)/(2)+2
Remove the parentheses around the expression y+1.
x=y+1_y+1=(y)/(2)+2
Since (y)/(2) contains the variable to solve for, move it to the left-hand side of the equation by subtracting (y)/(2) from both sides.
x=y+1_y+1-(y)/(2)=2
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 2. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
x=y+1_y*(2)/(2)-(y)/(2)+1=2
Complete the multiplication to produce a denominator of 2 in each expression.
x=y+1_(2y)/(2)-(y)/(2)+1=2
Combine the numerators of all expressions that have common denominators.
x=y+1_(2y-y)/(2)+1=2
Combine all like terms in the numerator.
x=y+1_(y)/(2)+1=2
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
x=y+1_(y)/(2)=-1+2
Add 2 to -1 to get 1.
x=y+1_(y)/(2)=1
Multiply each term in the equation by 2.
x=y+1_(y)/(2)*2=1*2
Simplify the left-hand side of the equation by canceling the common factors.
x=y+1_y=1*2
Multiply 1 by 2 to get 2.
x=y+1_y=2
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 2.
x=(2)+1_y=2
Remove the parentheses around the expression 2.
x=2+1_y=2
Add 1 to 2 to get 3.
x=3_y=2
This is the solution to the system of equations.
x=3_y=2
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! x-y=1
x=1/2y+2
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2x - 2y = 2
2x = y + 4
Sub for 2x in the 1st eqn
y+4 - 2y = 2
-y = -2
y = 2
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x-y = 1
x-2 = 1
x = 3
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It's a problem, not a doctoral dissertation.
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