How can I find 2 equations with infinitely many solutions? Thanks
You have to make them multiplies of each other.
For example: x+ y = 4
2x + 2y = 8
If you try to solve these equations, both sides reduce to 0. 0 = 0 True statement!! This means that any x and y that work in one equation will work in the other equation.
yes, buying more ticetks increase the chance of winning.chance means percent probability, 40% chance means out of ten trials i'll have 4 winningdon't know what is your lottery scheme, in canada they have this lotto 649, there are 6 numbers , 1..2..3.. up to 49 for each number1st prize winning all six numbers could have a jackpot of $10 million or morethe lottery probability equation is as followsA=[ (a)(a-1)(a-2)(a-3)(a-4)(a-5) ]B=[ (b)(b-1)(b-2)(b-3)(b-4)(b-5) ]X=A / BP=1 /Xa=max for each number, for lotto 649, a=49b=numbers of number per ticket, for lotto 649, b=6P=probability in decimalexample for lotto 649A=[ (49)(49-1)(49-2)(49-3)(49-4)(49-5) ]B=[ (6)(6-1)(6-2)(6-3)(6-4)(6-5) ]X=[10 068 347 520 ] / [ 720 ]X=13 983 816the probability to win 6 number with one ticket is PP = 1 / XP = 1 / 13 983 816P = ( 7.151E-8 ) or ( 7.151E-6 ) %for two ticetksP = 2 / Xfor three ticetksP = 3 / X - etcif you are familiar with excel, you can use excel formula= HYPGEOMDIST ( 6, 6, 6, 49 )= 7.15112E-8= 7.15112E-6 %in lotto 649, winning three numbers out of 6 number, you will get a prize of $10, the chance of winning $10 is as follows= HYPGEOMDIST ( 3, 6, 6, 49 )= 0.017 650 404= 1.76 %not too bad although it cost $2 per ticket
To find two equations with infinitely many solutions, you can use the concept of dependent equations.
A dependent equation is a system of equations where the two equations represent the same line or are multiples of each other. In other words, they have the same slope and intersect at every point along that line.
Here's a step-by-step process to create two equations with infinitely many solutions:
Step 1: Choose any equation with two variables. For example, let's say we have the equation:
2x + 3y = 6 (Equation 1)
Step 2: Multiply Equation 1 by a constant factor other than zero. Let's choose 2 as the constant:
4x + 6y = 12 (Equation 2)
Step 3: Equation 2 is now a multiple of Equation 1. It means that both equations represent the same line. They have the same slope and intersect at every point on that line.
For example, the slope-intercept form of Equation 1 is:
y = (-2/3)x + 2
And the slope-intercept form of Equation 2 is:
y = (-2/3)x + 2
As you can see, the equations are identical, and every point on this line satisfies both equations. Therefore, this system of equations has infinitely many solutions.
Remember, the key to creating two equations with infinitely many solutions is to make sure they represent the same line or are multiples of each other.