Question 346976: i'm trying to work on the process for this equation. i'm looking for the steps I can't remember how to work it through help
x=(4+y)/(3-y)
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! x=(4+y)/(3-y)
First, we can solve for Y
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(4+y)/(3-y)=x
Since the variable is in the denominator on the left-hand side of the equation, this can be solved as a ratio. For example, (A)/(B)=C is equivalent to (A)/(C)=B.
(y+4)/(x)=(-y+3)
Remove the parentheses around the expression -y+3.
(y+4)/(x)=-y+3
Find the LCD (least common denominator) of ((y+4))/(x)-y+3.
Least common denominator: x
Multiply each term in the equation by x in order to remove all the denominators from the equation.
(y+4)/(x)*x=-y*x+3*x
Simplify the left-hand side of the equation by canceling the common factors.
y+4=-y*x+3*x
Simplify the right-hand side of the equation by multiplying out all the terms.
y+4=-xy+3x
Since -xy contains the variable to solve for, move it to the left-hand side of the equation by adding xy to both sides.
y+4+xy=3x
Move all terms not containing y to the right-hand side of the equation.
xy+y+4=3x
Factor out the GCF of y from each term in the polynomial.
y(x)+y(1)=3x-4
Factor out the GCF of y from xy+y.
y(x+1)=3x-4
Divide each term in the equation by (x+1).
(y(x+1))/(x+1)=(3x)/(x+1)-(4)/(x+1)
Simplify the left-hand side of the equation by canceling the common factors.
y=(3x)/(x+1)-(4)/(x+1)
Simplify the right-hand side of the equation by simplifying each term.
y=(3x-4)/(x+1)
To solve for x
x=(4+y)/(3-y)
Reorder the polynomial 3-y alphabetically from left to right, starting with the highest order term.
x=(y+4)/(-y+3)
Now,
to find the x an y intercepts, you can :
x=(4+y)/(3-y)
To find the x-intercept, substitute in 0 for y and solve for x.
x=(4+(0))/(3-(0))
Remove the parentheses around the expression 0.
x=(4+0)/(3-(0))
Add 0 to 4 to get 4.
x=(4)/(3-(0))
Multiply -1 by the 0 inside the parentheses.
x=(4)/(3+0)
Add 0 to 3 to get 3.
x=(4)/(3)
To find the y-intercept, substitute in 0 for x and solve for y.
(0)=(4+y)/(3-y)
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(4+y)/(3-y)=(0)
Remove the parentheses around the expression 0.
(y+4)/(-y+3)=0
Find the LCD (least common denominator) of ((y+4))/((-y+3))+0.
Least common denominator: (-y+3)
Multiply each term in the equation by (-y+3) in order to remove all the denominators from the equation.
(y+4)/(-y+3)*(-y+3)=0*(-y+3)
Simplify the left-hand side of the equation by canceling the common factors.
y+4=0*(-y+3)
Simplify the right-hand side of the equation by multiplying out all the terms.
y+4=0
Since 4 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4 from both sides.
y=-4
These are the x and y intercepts of the equation x=((4+y))/((3-y)).
x=(4)/(3), y=-4
Hope this helps;-)
Jen
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