1. Solving Systems of Equations.
Elimination Method
Solving Systems of Equations.

2. 4x + 3y = 10 2x + y = 4 Elimination Substitution 1 2
Pick one of the variables you would eliminate. Find the LCM . Multiply equations to get the LCM and make sure they are opposite integers. Eliminate by adding.
Look for a variable with a coefficient
Of 1. Isolate that variable.
2x + y = 4
y = -2x + 4
Now substitute y with -2x +4 into the
first equation.
Want to eliminate
y variable. LCM = 3
4x + 3y = 10
Solve for y:
4 (1) + 3y = 10
4 + 3y = 10
3y = 6
y = 2
2x + y = 4
-3( 2x + y = 4)
= -6x – 3y -12
4x + 3 (-2x + 4) = 10
4x – 6x + 12 = 10
-2x + 12 = 10
-2x = -2
X = 1
Solve for y:
4 (1) + 3y = 10
4 + 3y = 10
3y = 6
y = 2
4x + 3y = 10
-6x – 3y = -12
-2x = -2
X = 1

3. Which one would you use? Substitution or Elimination or Both?
5t + 2d = 80
-5t – 20d = -350
2x + y = 3
4x + 3y = 5
6x + 7y = 10
2x - 3y = 14
X + 3y = -2
-3x + 5y = 6

4. Consistent, Inconsistent Systems Dependent, Independent Equations
(No Solution)
(1 or more solutions)
Consistent System
Inconsistent System
Dependent
Equation
All solution
Independent
Equation
1 or no solutions