As you go through your "math career," you will
come across equations that have more than one variable!
Although these may seem overwhelming, the idea is the
same - you are asked to rearrange the equation so that
the designated variable is isolated. The difference here is that
the answer will contain variables.
1. Solve for y: 6y - x + z = 4
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.
1. Solve for 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 Replaced 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).
Take the Quiz on multiple variable equations. (Very useful to review or to see if you've really got this topic down.) Do it!