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This is a simultaneous equation.
We want to get an equation that has just x's or just y's so that it can be solved. You need to have a look at both equations to work out which would be the easiest way.
In this case we are already told that y=5x+1 so all we have to do is substitute this into the equation.
So 8x + 2y = -2 becomes 8x + 2(5x + 1) = -2
So, 8x + 10x + 2 = -2
18x + 2 = -2
We now need to get x on one side of the equation and the number on the other.
As in all equations we must do the same thing on both sides
18x + 2 - 2 = -2 -2
18x = -4
x = -4/18 = -2/9
We now put this value of x back into one of the equations to find y - look for which one looks the simplest.
y = 5x+1 = -10/9 + 1 = -1/9
So the answer is that x=-2/9 and y= -1/9

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The question doesn't seem quite right!
If you wish to say that the perimeter is 70m and you want to find the length of each side then you can solve as follows.
A rectangle has opposite sides of equal length.
We can call the width x.
The length is 5m more than twice the width so we say that the length is 2x + 5.
The perimeter is the whole way round the rectangle which is x + 2x + 5 + x + 2x + 5 = 70m
So, 6x + 10 = 70
6x = 60
x = 10m and 2x + 5 = 25
so the dimensions of the rectangle are 10 x 25m.

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Your brackets seem to be in the wrong place.
Assuming that the question should be 6(t-5) = 2(t+5)
We want to find the value of t. To do this you need to get t on its' own on one side of the equation.
First you need to multiply out each side of the equation and lose the brackets.
6t - 30 = 2t + 10
Then you need to get all of the t's on one side and the numbers on the other.
Remember that what ever you do on one side you must do on the other
6t - 2t - 30 = 2t - 2t + 10
4t - 30 = 10
4t - 30 + 30 = 10 + 30
4t = 40
Now we have the t's on one side and the number on the other we can find out what t is.
To find out the value of t we divide each side by 4
4t/4 = 40/4
t=10
If you are ever worried about whether or not you have found the right answer, simply put it back into the original equation so in this case,
6(10-5) = 2(10+5)
6x5=30=2x15
Tip: If you have extra time in an exam always go back and do this just to make sure

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You need to find the surface area of the sides of the can.
Imagine that this label, before being wrapped around the can would actually be a rectangle.
The area of a rectangle is its' height x width.
The height is 13.2 cm.
The width is the the length of the paper going around the can which is the circumference of the can.
The circumference of a circle is given by the equation pi x D where D is the diameter of the can which is pi x 9.8
So the answer is pi x 9.8 x 13.2
So the area of the paper required is 406.4 cm sq.