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Archive Question #0131

I was in maths and Mr. Tyler set some homework about simultaneous equations. He said we had to answer: y= 1/2x +4, andy= 2x -1
What is he on about?
If you can help, I would be so grateful
Ta, Stephanie C.

Well, if a sun hat costs 3 pounds and the same sun hat costs 810 pesetas then you know that 3 pounds equals 810 pesetas. Or one pound equals 270 pesetas. In your equations, y is tha same as the sun hat. On the one hand y is equal to 1/2x+4 and on the other hand the same y is equal to 2x-1. So, just as you are able to remove the sunhat from the equation and say that 3 pounds equals 810 pesetas you can remove y from the equation and say that 1/2x+4 equals 2x-1. You now have an equation with only x's in and so can be solved quite easily to find out what x is.
1/2x+4=2x-1
1/2x+5=2x
5=2x-1/2x
5=3x/2
10 = 3x x=10/3 x=0.33333333333333333333333333333333333333 now that you have the value for x you can put it into either of the two original equations to find the value for y. I'll let you do that - though, are you quite sure you got the original equations right because the answer x=10/3 is an unusual one to give to simultaneous equation first timers? by the way, another way of solving this is to make a graph of the two lines. the solution to the simultaneous equations is the point where the two lines cross each other.

Brian

all u need 2 do is this..... u know that y=1/2x +4and u also know that y=2x-1.... therefore
1/2x +4 = y = 2x-1 so,
1/2x + 4 = 2x-1.
Commutative law means u can switch things from one side of the equals sign to the other by changing its sign ( + or -)...yes?? so it becomes
4+1 =2x -1/2x.
Which means that
5 = 1 1/2x to find x, u simply divide the 5 by 1 1/2.... then u can find what y equals from the original equations.