Find the value of x and y if 10x + y= 2xy-9.
There is no unique solution. This is just the equation of an hyperbola. Some integer solutions are
(-3,3)
(0,-9)
(1,19)
(4,7)
y = (10x+9)/(2x-1)
10x + y= 2xy-9
y - 2xy = -9 - 10x
y(1 - 2x) = -9-10x
y = (-9 - 10x)/(1 - 2x) or
y = ( 9+10x)/(2x-1)
pick any x you want, evaluate the y.
You can get as many values of x and y as you want.
The only value of x you can't choose is x = 1/2 , since for that value you would be dividing by zero.
e.g. let x = 1
y = (9+10(1))/(2(1) - 1)
= 19/1
= 19
so when x = 1, y = 19 or the ordered pair (1, 19)
etc.
To find the values of x and y in the given equation 10x + y = 2xy - 9, we need to solve for both variables. Here's how you can do it:
Step 1: Rearrange the equation.
Move all the terms involving x and y to one side and the constant term to the other side:
10x + y - 2xy = -9
Step 2: Combine like terms.
Arrange the terms in descending order by power of variables:
-2xy + 10x + y = -9
Step 3: Factor out common terms.
Factor out x and y from the left side of the equation:
x(-2y + 10) + y = -9
Step 4: Simplify the equation.
Expand the parentheses:
-2xy + 10x + y = -9
Step 5: Set up the system of equations.
Since the coefficients of x and y are different, we can set the coefficient of x in one equation equal to the coefficient of y in the other equation:
-2y + 10 = 1 (Coefficient of x = 1)
y = 11
Step 6: Substitute the value of y back into the equation to find x.
Substitute y = 11 into the original equation:
10x + 11 = 2x(11) - 9
10x + 11 = 22x - 9
Step 7: Combine like terms and solve for x.
Move all terms involving x to one side and all constant terms to the other side:
10x - 22x = -9 - 11
-12x = -20
x = (-20)/(-12)
x = 5/3 or approximately 1.67
Therefore, the values of x and y that satisfy the equation 10x + y = 2xy - 9 are x = 5/3 (or 1.67) and y = 11.