high school level
student is asking

y=4x	x=-4y
x+y=5	3x+2y=20

y=x-1	3x-y=4
x+y=3	2x-3y=-9






i tried divideing the two last numbers then subtracting the answer with the first number and i got them all wrong!!!!


For the problem

y = 4x
x + y = 5
the first equation tells you that y and 4x are the same. Thus, where you see y in the second equation you can replace it by 4x. Thus you get x + 4x = 5 In other words 5x = 5 and thus x = 1 Now use the first equation again. y = 4x and x is 1. Hence y = 4.

Thus the answer is x = 1 and y = 4.

In the problem

 x + 4y = 8
2x - 5y = 29
I see that the coefficient of x in the first equation is 1 and the coefficient of x in the second equation is 2. I would like the coefficient of x in both equations to be the same. I can accomplish this by multiplying both sides of the first equation by 2. That is 2(x + 4y) = 2(8) or 2x + 8y = 16 Thus the original two equations are equivalent to 2x + 8y = 16
2x - 5y = 29
The reason I wanted the two coefficients to be the same is that if I now subtract the two equations the coefficient of x becomes zero. That is (2x + 8y) - (2x - 5y) = 16 - 29 hence 2x + 8y -2x + 10y) = -13 Thus 18y = -13 and thus y = -13/18 Finally go back to either of the two equations you started with, replace y by  -13/18 and solve for x.

Now try the others.

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