Ray's New Elementary Algebra · Arts. 162–163 · Unit 4: Chapter IV: Simple equations
32. Three or more unknowns
Goal: Your student solves three equations in three unknowns by eliminating one unknown at a time.
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
- A card to cover printed answers
What's in the book
One set of three equations solved by all three methods, a four-unknown example, the general rule, exercises, then problems with three or more unknowns (the ingots worked out, exercises 2 to 15). Answers are printed.
The lesson, step by step
Warm-up
Solve x + y = 7 and 2x − y = 5 quickly. (4 and 3.)
Work the book's example
Follow "Solution by addition and subtraction" on p. 127: x + 2y + z = 20, 2x + y + 3z = 31, 3x + 4y + 2z = 44. Eliminate x twice to get 3y − z = 9 and 2y + z = 16; add to get y = 5; then z = 6 and x = 4.
The general rule
1. Eliminate the same unknown quantity from each of the equations; the number of equations and of unknown quantities will be one less.
4. By going back and substituting, the values of the other unknown quantities may be readily found.
Read all four steps aloud.
Guided practice
Your student solves the first exercise on p. 129 (x + y = 50, x + z = 28, y + z = 42; answer 18, 32, 10) while you watch. Hint: add all three first.
Problems
Your student sets up and solves:
2. The sums of three numbers, taken two and two, are 27, 32, and 35 ; required the numbers. Ans. 12, 15, and 20.
Then read the worked ingot problem 1 together.
Independent practice
The other exercises on pp. 129 and 130, and three or four of problems 3 to 15 (6 and 11 are good).
Wrap-up
Use the General Review on p. 134 as a quiz on the whole chapter.
Tip
Keep the work in a tidy column with numbered equations. With three unknowns, neatness is half the battle.
Answers to the book's problems
The book prints the answer after each exercise.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in the Key ↗.