The solution is a two-step process:
1). Draw the graph of the function. On a piece of graph paper, draw a set of
x/y axes. Then with your pencil, make a dot on the y-axis where y=100, and
another dot on the x-axis where x=12.5 . Now place your ruler against the
two dots, and taking hold of your pencil again, connect the two dots, and
extend the line as far as you can in both directions. Technically, it goes on
forever in both directions, and never ends.
Now you're ready to solve the equation.
2). Every point on the line you drew is a pair of numbers ... 'x' and 'y' ... that is
a solution to the equation. How many are there ? Don't try to list them, as the
list is infinite. That's what's so great about the graph ... it shows an enormous
number of solutions with one simple picture.
x + 8x = 477 9x = 477 x = 53
8x+39 = 2x-15 6x = -54 x = -9
x=1, y=1
-8x + 3 = 251 -8x = 251 - 3 -8x = 248 -x = 248 ÷ 8 -x = 31 x = -31
(4 ± i2) where i2 = -1
8x + -2 = 10 8x = 12 x = 1.5
16x - 8x + 12 = 78 + 22 or simplified to (16x-8x=8x)(78+22=100) 8x + 12 = 100 Simplify some more (Subtract 12 from both sides) 8x = 88 Divide both sides by 8, and x = 11
x + 8x = 477 9x = 477 x = 53
-8x + 6 = -58 -8x = -64 x= -64/-8 x = 8
x= -8
8x+39 = 2x-15 6x = -54 x = -9
x=1, y=1
Y-8x plus 9y equals 10y-8x.
-8x + 3 = 251 -8x = 251 - 3 -8x = 248 -x = 248 ÷ 8 -x = 31 x = -31
8x = 2x + 15 6x = 15 x = 15/6 = 2.5
4x + 3y = 8x + y so 3y - y = 8x - 4x ie 2y = 4x so y = 2x
(4 ± i2) where i2 = -1