Math 141 Lecture Notes for Section 2.1
Section 2.1 -
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Systems of Linear Equations
Previously, in section 1.4 we solved the intersection of two lines. Examples such as this we used the
slope-intercept form of two linear equations to solve for their intersection. In this section, we are
going to explore another method of solving these types of problems. We draw our motivation from the
following problem.
Example 2.1.1:
Suppose we have two linear equations
L1 : 2x + 6y = 8
L2 : 4x − 3y = 2
and we want to find their intersection.
Math 141 Lecture Notes for Section 2.1
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Example 2.1.2:
As a third example, consider the system of linear equations:
L1 : 2x +4y
L2 : 3x +6y
=9
= 12
Math 141 Lecture Notes for Section 2.1
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An equation of the form
Ax + By + Cz = D
where A, B, C, and D are all constants and not all of A, B, and C are zero is the equation of a plane.
We can also solve systems of equations in three variables using the methods explored in the three
examples above. In fact, we aren’t limited to three variables, we can use as many variables as we like.
We are still limited by the possibilities of one, zero, or infinitely many solutions.
Example 2.1.3:
Consider the following equations
P1 : 2x
P2 : x
P3 : 3x
+3y
+2y
+4y
Find their point or points of intersection (if it exists)
+5z
−4z
−z
=6
=1
= −4
Math 141 Lecture Notes for Section 2.1
Suggested Homework Problems: 5, 7, 9, 11, 19, 23, 27, 31, 35, 37, 39.
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