could anyone please show me a detailed method you could use for solving these simultaneous equations
12x + 65y - 1 = 0 and
60y = 150x + 511
thanks for any help
i don't know what you mean by isolating a single variable. i've only started maths recently. i have tried things, like rearranging the top equation to match the bottom one in order. then make the x's or y's the same number and cancel them out. but i end up with 138 and 12/13 x = 511 and 12/13
It means make it something like x = f(y) or y = f(x)
For example: $\displaystyle 12x +65y-1 = 0$
Add 1 to both sides and take 65y from both sides: $\displaystyle 12x = 1 - 65y$
Divide by 12: $\displaystyle x = \frac{1}{12}(1-65y)$
Now that x is expressed in terms of y you can put this into equation 2 wherever you see x
Not sure what/why you're asking, Mark.
From 12x + 65y - 1 = 0 we get x = (1 - 65y) / 12
We substitute that in 60y = 150x + 511, to get:
60y = 150(1 - 65y) / 12 + 511
Solving gives y = 1047/1745 = 3/5
Substituting y = 3/5 in 12x + 65y - 1 = 0 results in x = -19/6 or -3 1/6