About Solving Systems of Linear Equations by Graphing:

When we solve a system of linear equations by graphing, we begin by graphing each equation. We then look to find the point of intersection. This point satisfies both equations and is therefore the solution to the system. Graphing is the least efficient method to use. In most cases, we want to use an algebraic method such as substitution, or elimination.


Test Objectives
  • Demonstrate the ability to graph a linear equation in two variables
  • Demonstrate the ability to find the point of intersection
  • Demonstrate the ability to check the solution for a system of linear equations
Solving Systems of Linear Equations by Graphing Practice Test:

#1:

Instructions: Solve each linear system by graphing.

a) $$3x + 2y = 8$$ $$x - 4y = 12$$


#2:

Instructions: Solve each linear system by graphing.

a) $$13x - 3y = -18$$ $$2x - 3y = 15$$


#3:

Instructions: Solve each linear system by graphing.

a) $$6x - 7y = 28$$ $$2x - \frac{7}{3}y = \frac{49}{3}$$


#4:

Instructions: Solve each linear system by graphing.

a) $$17x - 3y = 27$$ $$2x - 3y = -18$$


#5:

Instructions: Solve each linear system by graphing.

a) $$10x - 7y = -21$$ $$2x - 14y = 84$$


Written Solutions:

#1:

Solutions:

a) {(4,-2)} : x = 4, y = -2

Solving a system of linear equations by graphing

#2:

Solutions:

a) {(-3,-7)} : x = -3, y = -7

Solving a system of linear equations by graphing

#3:

Solutions:

a) No solution : ∅

Solving a system of linear equations by graphing

#4:

Solutions:

a) {(3,8)} : x = 3, y = 8

Solving a system of linear equations by graphing

#5:

Solutions:

a) {(-7,-7)} : x = -7, y = -7

Solving a system of linear equations by graphing