1. Determine which of the two equations is the easiest to solve for a variable if it hasn’t already been solved for.
2. Meaning it must look like:
x=
y=
3. Then substitute what the variable is equal to in the other
equation.
4. Solve for the given variable and the plug that number back into an equation to solve for the other variable.
Example: x + y = 3 x = 2y
2y + y = 3
3y = 3 y = 1
Set the equations up and determine which one is easiest to solve for.
The second equation is already solved for (x).
Replace (x) in the first equation with 2y and then solve for (y).
Plug in the value for (y) in x + y = 3 x + 1 = 3 x = 2 any of the two equations and solve for (x).
Answer: (2,1)

Example:
4x + y = 11
2x + 5y = 1 y = -4x +11
2x + 5(-4x+11) = 1
2x + -20x +55 = 1
-18x + 55 = 1
-18x = -54 x = 3
4x + y = 11
4(3) + y = 11
12 + y = 11 y = -1
Set up the equations to see which one is going to be easiest to solve for.
The first equation is the easies because the (y) has no coefficient.
Solve the first equation for
(y)
Now replace (y) in the second equation with what it is equal to.
Distribute and then combine like terms.
Solve for (x).
Pick any equation with both the (x) and (y) and replace
(x) with 3 and solve.
Answer: (3,-1)
Updated 2-16-09