SYSTEMS OF LINEAR EQUATIONS

AND INEQUALITIES

Week 02: Solving System of Linear Equations Graphically Prepared by: Jojo M. Lucion

DISCUSSION

Two or more equations such as x + y = 10 and x - y = 2 form a system of linear

equations. To solve such a system, we find the ordered pair that makes both equations true. To

solve a system of linear equations graphically, graph each equation on the same set of coordinate

axes. For two lines that intersect at a point, the coordinates of that point are the solution of the

system.

Example 1.

Graph : x + y = 10

x-y =2

You can form table of values then graph.

To solve a system of linear equations graphically, graph each equation on the

same set of coordinate axes. For two lines that intersect at a point, the

coordinates of that point are the solution

What is the intersection of the two lines? (6, 4 )

(6, 4 ) is the solution set.

We can check that ( 6, 4 ) is the solution set by verifying that x = 6 and y = 4 makes both of the

original equations true at the same time.

Example 3. Solve the system by graphing

2x + y = 5

y - x = -4

Transform the equations into y = mx + b

Each equation can be graphed using the slope - intercept method. As shown in the figure, what

is the solution of the system of equations? Why?