Section 4.1
Solving Systems of Linear
Equations in 2 Variables
Vocab
 A System of Equations is a group of 2 or more
equations.
 The Solution to a system is the order set of
numbers that makes all of the equations true.
 To Check a Solution, substitute the variables in
for x and y into EACH equation and verify. IF all
equations work out, then it is a solution
To Solve by GRAPHING:
 1. Graph both equations on the same coordinate
plane.
 2. The solution is the point where the 2 lines
intersect. (Consistent with independent equations)
 3. If the lines are parallel, there is no solution.
(Inconsistent system)
 4. If the lines are identical, there are infinitely
many solutions. (Consistent with dependent
equations)
To Solve by SUBSTITUTION:
 1. Select one equation and isolate one of the
variables.
 2. In the other equation, substitute the
expression for step 1 for that variable.
 3. Solve this new equation.
 4. Substitute the value found in step 3 into
the first equation to find the other variable.
 5. Check the solution in the original
equations.
To Solve by ELIMINATION:
 1. Write both equations in standard form.
 2. Multiply one or both equations so that either x
or y have OPPOSITE coefficients.
 3. Add the equations together to eliminate a
variable
 4. Solve the resulting equation.
 5. Substitute the value found in step 4 into the
either of the original equations to find the other
variable.
 6. Check the solution in the original equations.