2x + 3y = 1
y = 3x + 15
There's not much you can do with the first equation, because it has
two variables in it ... 'x' and 'y' . No matter how much you move them
around, you'll never be able to get either one equal to just a number.
Is there any way you could get rid of one of the variables in the first
equation, and have just 1 letter in it to solve for ?
Absolutely ! The second equation tells you something that 'y' is equal to,
(3x + 15). "EQUAL" is very powerful. It means that wherever you see 'y',
you can put (3x + 15) in its place, and you won't change anything or
upset anything. One thing you can do is take that (3x + 15) from the
2nd equation, and put it right into the first equation in place of 'y'.
You'll see how that helps as soon as you do it.
First equation: 2x + 3y = 1
Substitute for 'y' : 2x + 3(3x + 15) = 1
Remove parentheses: 2x + 3(3x) + 3(15) = 1
2x + 9x + 45 = 1
Combine the terms with 'x' in them: 11x + 45 = 1
Look what you have now ! An equation with only one variable in it !
Subtract 45 from each side: 11x = -44
Divide each side by 11 : x = -4
You're more than halfway there. Now you know what 'x' is,
and you can use it with either equation to find what 'y' is.
-- If you use it with the first equation: 2x + 3y = 1
Put in the value of 'x': 2(-4) + 3y = 1
Remove the parentheses: -8 + 3y = 1
Add 8 to each side: 3y = 9
Divide each side by 3 : y = 3
-- If you use it with the 2nd equation: y = 3x + 15
Put in the value of 'x' : y = 3(-4) + 15
Remove the parentheses: y = -12 + 15
Add numbers on the right side: y = 3 (same as the other way)
So there's your solution for the system of two equations:
x = -4
y = 3
