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
x+5y=4
3x+15y=-1
x+4y=8
2x-5y=29
2x-3y=-24
x+2y=15
x-5y=10
2x-10y=20
4x+y=0
x+2y=-7

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

Hi,
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.

Cheers,

Penny