Solve by using the ELIMINATION method The goal is to eliminate one of the variables by performing multiplication on the equations, and then add the two equations together. Solve a System of Equations

How to eliminate a variable? Example of a system is below: 3x + 4y = 5 2x – 6y = 12 To eliminate the x variable, we can multiply the first equation by -2, and the second by 3.

Solve a System of Equations The result would be: -2 [3x + 4y = -8]  -6x – 8y = 16 3 [2x – 6y = 12]  (+) 6x – 18y = 36 Now the x variable will cancel if we add the two equations. Now we are only left with the y-variable. We certainly know how to solve -26y = 52.

Solve a System of Equations Now we will solve a slightly more easy problem for you since we are just starting this topic. Sample problem is below: x + y = 3 (first equation) 3x + y = 3 (second equation)

Solve a System of Equations x + y = 3 (first equation) 3x + y = 3 (second equation) The goal is to “eliminate” one of the variables. Variable must have the same number but opposite signs.

Solve a System of Equations x + y = 3 3x + y = 3 (same number, but signs are not opposite. Fix it!) -1[3x + y = 3]  multiply by every term by -1. The new equation is below: -3x – y = -3  new equation to use in our problem

Solve a System of Equations Now we can add the two equations together. x + y = 3 (first equation that was not touched) (+) -3x – y = -3 (new equation, from multiplying) -2x = 0 (divide by -2 on both sides) x = 0 (this is only half our answer… )

Solve a System of Equations Now, use the original equations to find the second part of your answer. x + y = 3 (first equation) 3x + y = 3 (second equation) since “x = 0” is part of our answer, use it!) 0 + y = 3 y = 3

Solve a System of Equations For the system of equations problem: x + y = 3 (1 st original equation) 3x + y = 3 (2 nd original equation) Final solution is (0, 3) This means that these two linear equations intersect at (0, 3).

Solve a System of Equations Check for understanding… To eliminate the x variable, what should you multiply by for the below problem? 2x + 4y = 12 x + 3y = 5

Solve a System of Equations Anwer…. Mulitply the bottom equation by -2, and then add the two equations together. 2x + 4y = 12  2x + 4y = 12 -2[x + 3y = 5]  -2x – 6y = -10 You need to practice at least 20 problems. Now, let’s get the practice in so that we become experts at this!