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Hello, can someone help me sovle these, i know the gaussian and substitution methods but the coefficients in these equations are all proportional so when i multiply up to cancel out it removes all Xs and all Ys, any suggestions are welcome, it's probably really simple and i'm missing something, thanks guys.
10x+2y=8 and;
3y+15x=12
thanks again :).
10x+2y=8...(1)Quote:
Originally Posted by captainlewis
15x+3y=12...(2)
Equation (1) and (2) are really the same. To see this multiply (1) by 15.
Work with equation (1).
10x+2y=8
Thus,
5x+y=4
Thus,
y=-5x+4
Let x=t i.e. and real number.
Then, y=-5x+4=-5t+4
Thus,
x=t
y=-5t+4
Are all solutions.
Hello, captainlewis!
You're not missing a thing.
. . The system does not have a unique solution.
Quote:
10x + 2y .= .8 . [1]
15x + 3y .= 12 -[2]
Divide [1] by 2: .5x + y .= .4
Divide [2] by 3: .5x + y .= .4
You see, they gave us only one equation.
And one equation with two variables has an infinite number of solutions.
It says: "Find two numbers x and y so that 5 times x plus y equals 4"
. . and there are zillions of answers: .(1,-1), (0,4), (-1,9), . . .