About Solving Systems of Linear Equations by Elimination:

When we solve a system of linear equations, it is often necessary to use an algebraic method. Another such method is known as elimination. With this method, we transform one pair of variable terms into opposites. We then add the two equations together and eliminate one of the variables. We can then proceed to solve our system.


Test Objectives
  • Demonstrate the ability to create one pair of opposite variable terms
  • Demonstrate the ability to eliminate one of the variables from a two variable linear system
  • Demonstrate the ability to solve a linear system using elimination
Solving Systems of Linear Equations by Elimination Practice Test:

#1:

Instructions: Solve each linear system by elimination.

a) $$4x + 3y = 5$$ $$9y = -12x$$


#2:

Instructions: Solve each linear system by elimination.

a) $$x + 6y = -14$$ $$-4x = -12y + 20$$


#3:

Instructions: Solve each linear system by elimination.

a) $$-24 = -32y + 40x$$ $$-100x = 60 - 80y$$


#4:

Instructions: Solve each linear system by elimination.

a) $$-32 - 9x = -5y$$ $$-5x = 30 - 4y$$


#5:

Instructions: Solve each linear system by elimination.

a) $$4x = 1 - 3y$$ $$-3x - 5y = -9$$


Written Solutions:

#1:

Solutions:

a) No solution : ∅


#2:

Solutions:

a) {(-8,-1)} : x = -8, y = -1


#3:

Solutions:

a) {(-∞,∞)} : infinitely many solutions


#4:

Solutions:

a) {(2,10)} : x = 2, y = 10


#5:

Solutions:

a) {(-2,3)} : x = -2, y = 3