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Read the explanation in each lesson carefully, then study the examples given before doing the exercises.
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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?