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Example 5.40 from Elementary Algebra, 5.4 Solve Applications with Systems of Equations
Solve Applications with Systems of Equations: example 5.40
Translate to a system of equations and then solve:
Two angles are supplementary. The measure of the larger angle is twelve degrees less than five times the measure of the smaller angle. Find the measures of both angles.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Step 1. Read the problem. Step 2. Identify what we are looking for. We are looking for the measure of each angle. Step 3. Name what we are looking for. Let the measure of the first angle.
the measure of the second angleStep 4. Translate into a system of equations. The angles are supplementary. The larger angle is twelve less than five times the smaller angle The system is:
Step 5. Solve the system of equations substitution.Substitute 5x − 12 for y in the first equation. Solve for x. Substitute 32 for in the second equation, then solve for y. Step 6. Check the answer in the problem. Step 7. Answer the question. The angle measures are 148 and 32.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Translate to a system of equations and then solve:
Two angles are supplementary. The measure of the larger angle is 12 degrees more than three times the smaller angle. Find the measures of the angles.
How did it go?