First you need to understand what "solve" means, so that you'll know a solution when you see it.
A "solution" to an equation means a number that you can write in place of the
variable (the letter) and have the equation be true.
If the equation has two variables in it, line 'x'and 'y', then a solution is a set of
two numbers ... one for 'x' and one for 'y' ... that you can write in their places
and have the equation be true. That's the kind of equation you have here.
A solution to this equation is a pair ofnumbers ... one for 'x' and one for 'y' ...
that we can write in their places and have the equation be true.
Now, you may have learned that an equation with 'x' and 'y' in it can be drawn
as a graph. The part you have to think about until it blows your mind is this:
EVERY POINT on that graph has an 'x' number and a 'y' number for its
location on the graph, and every one of those pairs of (x, y) numbers is
a solution to the equation !
Here, let me show you examples.
Pull a number out of the air for me.
Did you say ' 1 ' ? Fine. 'x' is ' 1'.
Take the equation: y = 50x + 10
Put '1' in the place of 'x': y = 50(1) + 10
y = 50 + 10
y = 60
There's one pair of numbers: x=1, y=60.
Throw another number at me. Any number.
Did you say zero ? Great 'x' is zero now.
Take the equation: y = 50x + 10
Put '0' in the place of 'x': y = 50(0) + 10
y = 10
There's another pair of numbers: x=0, y=10.
Both of these pairs of numbers are solutions to your equation. You can
find as many more solutions as you want. Just pull a number out of the
air, write it into the equation in place of 'x', figure out what 'y' is, and there
you have another solution !
There are an infinite number of them ... every point on the graph,remember ?
