4xy²(3y-x)-2x²(x-3y)²=4xy²(x-3y)-2x²(x-3y)²=(x-3y)[4xy²-2x²(x-3y)²]=(x-3y)(4xy²-2x³+6x²y)=(x-3y)(-2x³+6x²y+4xy²)=-2x(x-3y)(x²-3xy-2y²)= -2x(x-3y)(x-y)(x-2y)
3xy + 3y2 = 3y (x + y)
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3y2 y x y = y2 3 x y2 = 3y2
X + 3y - 2y + 3y = X + (3-2+3)y = X + 4y
4xy²(3y-x)-2x²(x-3y)²=4xy²(x-3y)-2x²(x-3y)²=(x-3y)[4xy²-2x²(x-3y)²]=(x-3y)(4xy²-2x³+6x²y)=(x-3y)(-2x³+6x²y+4xy²)=-2x(x-3y)(x²-3xy-2y²)= -2x(x-3y)(x-y)(x-2y)
y = x/(x - 3) so y(x - 3) = x xy - 3y = x xy - x = 3y x(y - 1) = 3y x = 3y/(y - 1) for y ≠1 So, the inverse function is f(y) = 3y/(y - 1) where y ≠1
3xy + 3y2 = 3y (x + y)
The problem to solve is: xy+x+3y+3 Multiply y and x Multiply the y and x Multiply y and x The y just gets copied along. The x just gets copied along. The answer is yx yx x*y evaluates to yx x*y+x evaluates to yx+x Multiply y and 3 Multiply y and 1 The y just gets copied along. The answer is y y 3*y evaluates to 3y The answer is yx+x+3y x*y+x+3*y evaluates to yx+x+3y The answer is yx+x+3y+3 x*y+x+3*y+3 evaluates to yx+x+3y+3 ---- The final answer isyx+x+3y+3----
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If x - 3y = 12, we can solve for x in terms of y: x = 12 + 3y. Then, to find xy, we multiply x by y: xy = y(12+3y) = 12y + 3y^2.
3y2 y x y = y2 3 x y2 = 3y2
X + 3y - 2y + 3y = X + (3-2+3)y = X + 4y
x + y = 6 so that -x = y - 6 -x + 3y = -2 that is, y - 6 + 3y = -2 or 4y = 4 or y = 1 and then -x = y - 6 = -5 so that x = 5
y=3(2+x) y= 6+3x Switch x and y x = 6+3y solve for y x-6 = 3y 3y = x-6 y = (x-6)/3 f^-1(x) = (x-6)/3 is the inverse function.
x+7x+3y-y =8x+2y =2(4x+y)
6x - 3y = 36 x intercept: If y = 0, then 6x=36 so x=6 y intercept: If x = 0, then -3y=36 so y = -12