Download Math 251: Beginning Algebra Section 4.1 Notes Solving Systems of

Math 251: Beginning Algebra
Section 4.1 Notes
Solving Systems of Linear Equations by Graphing
Recall, an equation in two variables is linear provided it can be written in the form:
Ax + By = C
A system of linear equations is a grouping of two or more linear equations.
Definition:
Examples:
(a)
(b)
A solution of a system of linear equations is an ordered pair that makes both equations true at the
same time. A solution of an equation is said to satisfy the equation.
Example 1: Decide whether the ordered pair (4,−1) is a solution of each system.
(a)
(b)
5 x + 6 y = 14
2x + 5 y = 3
− x − y = −3
x + y = −3
Math 251: Beginning Algebra
Section 4.1 Notes
A system of two equations containing two variables represents a pair of lines.
The points of intersection are the solutions of the system.
Hence, we can look at their graphs to solve the system! Their graphs can appear in one of 3 ways:
Intersect at exactly one point
Parallel
They are the same line
One solution
No solution
Infinite number of solutions
Example 2: Solve the system by graphing.
2x − y = 4
4x + y = 2
Math 251: Beginning Algebra
Section 4.1 Notes
Example 3: Solve the system by graphing.
x + 2y = 4
2 x + 4 y = 12
Example 4: Solve the system by graphing.
2x − y = 4
4x = 2 y + 8