Example:
1. Solve for y: 6y - x + z = 4
Solution: Begin by isolating y by adding x and
subtracting z from both sides.
6y - x + z = 4 Original equation.
+ x - z = 4 + x - z Add (x - z) to
---------------------- both sides.
6y = 4 + x - z
Divide each term by 6.
6y 4 x z
-- = - + - - -
6 6 6 6
2 x z
y = - + - - -
3 6 6
As you can see above, this process doesn't do much good because you still have variables in the
answer. However, when you have more than one equation with the same variables, you can use the process
described above to solve for all the variables and get a constant for an answer. When you have two or more
equations that call for the same solution, you have a system of equations.
When solving systems of equations, always remember that if a = b, you can substitute b for a or a for b.
Example:
1. Solve: 3x + 2y = 3 and x = 3y - 10
Solution: Replace x in the first equation with its equivalent,
(3y - 10) from the second equation.
3x + 2y = 3 Top equation.
3(3y - 10) + 2y = 3 Replace x with (3y - 10).
9y - 30 + 2y = 3 Multiplied out.
11y = 33 Simplified.
y = 3 Divide each side by
11 to get answer.
Now that y has a value, you can plug
that value in either equation and find
a value for x.
Because the second equation has already
been solved for x, it will be easier to
plug 3 in for y in that equation.
x = 3(3) - 10
x = 9 - 10
x = -1
The solution is the ordered pair (-1, 3).
Back to top.
Take the quiz on multiple variable equations. The quiz is very useful for either review or to see if you've really got the topic down.