General Contents
Detailed Contents
Index
Programmed tutorial: Elimination Method for Linear Systems: Example 1
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Use the
Elimination Method
to solve
x + 2y = 1
Equation 1
x y = 4
Equation 2
General Contents
Detailed Contents
Index
How do we proceed?
We want to manipulate these equations so that one variable is eliminated. Lets eliminate x.
How can we do that by working on equation 2?
We can multiply equation 2 by (-1) and then add the result to equation 1.
Do that.
We multiply all terms on both sides of equation 2 and get
x + y = 4
Now set up the addition of equation 1 and this new equation.
x + 2y = 1
x + y = 4
Add the equations.
We get 3y = 3.
Solve.
Dividing by 3 on both sides, we have
y = 3/3 = 1
Are we done?
No.
What else must we do?
Since a solution is an (x, y) pair, we need to find the corresponding value of x.
How do we do that?
We substitute this value of y into either of the original equations.
Do that using equation 1.
Using
equation 1 and y = 1, we get
x + 2y = x + 2(1) = 1
Simplify.
x 2 = 1.
Solve.
Add 2 to both sides to get
x = 1 2 = 3.
Summarize these results.
The original equations
x + 2y = 1
Equation 1
x y = 4
Equation 2
have the point (3, 1) as a solution.
Do we need to check our results?
Yes.
In
both
original equations?
Yes.
Do it.
Using x = 3, y = 1, check Equation 1.
Equation 1: x + 2y = 3 + 2(1) = 3 2 = 1 OK.
Now check Equation 2.
Equation 2: x y = 3 (1) = 3 + 1 = 4 OK
What is the graphical interpretation of these results?
Each equation graphs as a line. The solution is the intersection of the lines.
Plot the lines on paper and then check your graph by clicking the Next button.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
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