3
To find two numbers that add to 3 and multiply to 18, we can set up a system of equations. Let's call the two numbers x and y. We have the equations x + y = 3 and x * y = 18. By solving this system, we can find that the numbers are 1.5 and 12.
Sum of digits x+y=8 Two digit no assume as 10x+y It is given that 10x+y+18=10y+x 9x-9y+18=0 x-y=-18/9 x-y= -2 Equate both x+y-8=x-y+2 2y=10 y= 5 Substitute this y in x+y x+5=8 x=3 So 35 is original two digit no Reversed new no is 53
2x + 5y = 2-3x - y = -3from the second equation:-y = -3 + 3xy = 3 - 3xsubstitute this value in the first equation:2x + 5(3-3x) = 22x + 15 - 15x = 2-13x + 15 = 2-13x = 2 - 15-13x = -13so, x = 1Now, solve for y :y = 3 - 3xy = 3 - 3 (1)y = zero
Let's denote the two numbers as x and y. We can set up a system of equations: x + y = 18 and x - y = 4. By solving this system simultaneously, we can find that x = 11 and y = 7. Therefore, the two numbers that add up to 18 and subtract to 4 are 11 and 7.
103
13x
if and x equal -18 find y -18 * 1/3 = -6
Let x and y be positive numbers such that xy=13. Thus, y=13/x. We want to minimize t=x+y=x+13/x. Differentiate t=x+13/x. t'=1-13x-2 Set this equal to zero. 1-13x-2=0 13x-2=1 x2=13 x=sqrt(13) Now solve for y: y=13/x=13/sqrt(13)=sqrt(13)
If y(x) = 1/3x, y(-18) = 1/[3(-18)] = -1/54.
If y varies directly as x and y is 18 when x is 24, then y is always three fourths of x. So if y is 15, then x is 20.
x=-16 , y= -31/3
2x + 5y = 2 ..... Eq.1-3x - y = -3 ..... Eq.2 .... we can write it in another form y = 3 - 3xPut the value of y in Eq.1 the result will be :2x + 5(3 - 3x) = 22x + 15 - 15x = 22x - 15x + 15 = 2-13x + 15 = 2-13x = 2 - 15-13x = -13x = -13/-13 ......... X = 1to find Y, put the value of X in Eq.2y = 3 - 3xy = 3 - 3(1)y = 3 - 3 .......... Y = Zero
17
That equation represents only one line. y - 11 = 13x - 7 y = 13x + 4 The slope is 13.
That equation represents only one line. y - 11 = -13x - 7 y = -13x + 4 The slope is -13.
If x and y are the two angles, then x + y = 90 and x - y = 18 Adding the two equations together gives 2x = 108 so that x = 54 and then y = x - 18 = 36