Programmed tutorial: Elimination Method for Linear Systems: Example 4

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Use the Elimination Method to solve

Equation 1

Equation 2

General Contents

Detailed Contents

Index

Here we have a mixture of fractions and decimals. What is the least common denominator for clearing the fractions?

Multiply both sides of equation 1 by 10 to clear the denominators.

2x + y = 4.25 Equation 3
4x + 5 y = 9.25 Equation 4

How should we proceed to use the elimination method?

To eliminate y, we can multiply equation 3 by (–5).

Do it.

Our equations become
(–5)*(2x +y ) = (–5)*4.25, or
–10x – 5y = –21.25, and
4x + 5y = 9.25

Add the equations.

We get
–6x = –12, or
x = 2

Use this result to solve equation 3 for y.
2x + y = 4.25 becomes
2*2 + y = 4.25, or
y = 0.25

Summarize our work thus far.

The point given by x = 2, y = 0.25 is the solution to the original equations.

How can we check these results?

We can substitute them in the original equations.

Do we need to check in both equations?

Yes.

In equation 1,

, we get

0.4 + 0.025 = 0.425; Checks

In equation 2,

, we get

0.8 + 0.125 = 0.925; Checks

The end. If you found this helpful and would recommend that I create more pages like this one, please let me know: Email to John Taylor