x = 4y 3x - 2y = 20 Substituting the value of x into the second equation, 3*(4y) - 2y = 20 ie 12y - 2y = 20 or 10y = 20 so that y = 2 Then x = 4y = 4*2 = 8. So (x , y) = (8 , 2)
y = 3x + 2 y-2 = 3x x = (y-2)/3 So the inverse is (x-2)/3
3x^2 - 27 = = 3(x^2 - 9) = 3(x^2 - 3^2) = 3(x - 3)(x + 3)
y = 3x - 2 3x = y + 2 x = y + 2 --------- 3
5=3x+2 3x+2-2=5-2 3x=3 ------ 3 x=1
x-2=3x+1 x=3x+1+2 x-3x=3 -2x=3 x=-3/2
3x + 4y = 5x - 2y = 5leads to:x = 5 + 2ySo:3(5 + 2y) + 4y = 515 + 10y = 510y= -10y=-1and therefore if y = -1 then x = 3.
(x^2-2) (x^2+3x+5)= x^2(x^2+3x+5) -2(x^2+3x+5)= x^4 +3x^3 +5x^2 -2x^2 -6x -10= x^4 +3x^3 +3x^2 -6x -10
(x^3 + 2x^2 + 3x - 6)/(x - 1) add and subtract x^2, and write -6 as (- 3) + (-3) = (x^3 - x^2 + x^2 + 2x^2 - 3 + 3x - 3)/(x - 1) = [(x^3 - x^2) + (3x^2 - 3) + (3x - 3)]/(x - 1) = [x^2(x - 1) + 3(x^2 - 1) + 3(x - 1)]/(x - 1) = [x^2(x - 1) + 3(x - 1)(x + 1) + 3(x - 1)]/(x - 1) = [(x - 1)(x^2 + 3x + 3 + 3)]/(x - 1) = x^2 + 3x + 6
y=(x+2)/(x+10) xy+10y=x+2 xy-x=2-10y x(y-1)=2-10y x=(2-10y)/(y-1)
-3x + 2 = -7 - 2 -2 -3x = -9 so x = 3
If x = 8 and y = 10 then it is 44.
3x^2+3x-60=3(x^2+x+20)=3(x+5)(x-4)
-2x-10y-12+3xy=4Put all x's to the other side and the ones with y's on the other:-10y+3xy=4+2x+12-10y+3xy=16+2xNow you factor a y from the side with the y's:y(-10+3x)=16+2xDivide both sides by (-10+3x):y=(16+2x)/(-10+3x)
3x - 2y = 20 Substitute x = 4y into this equation: 3(4y) - 2y = 20 ie 12y - 2y = 20 10y = 20 so that y = 2 and then x = 4y gives x = 2*4 = 8
x = 4y 3x - 2y = 20 Substituting the value of x into the second equation, 3*(4y) - 2y = 20 ie 12y - 2y = 20 or 10y = 20 so that y = 2 Then x = 4y = 4*2 = 8. So (x , y) = (8 , 2)
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