Key to Greenleaf's Algebra

Cover Key to Greenleaf's Algebra
Key to Greenleaf's Algebra
Benjamin Greenleaf
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2. Transposing, 2z=25— 3y.
3. Dividing, s=12— y — ^.
4. Changing terms, £=12— 2y-f 5. Substituting, w=^X-.
2 INDETEBMINATE ANALYSIS. 189 6. Clearing of fractions, 2»=y+l.
7. Transposing, y=2w— 1.
8. Putting the value of y into (4), x=12— 2(2rc— l)+n.
9. Uniting terms, a=14 — 3rc.
Let n = 1, then a: = 11, and y = 1.
7i = 2, " s = 8, " y = 3.
n = 3, " a; = 5, " y = 5.
n = 4, " a: = 2, « y = 7.
That is, 11 two-dollar bills, and 1 three-dollar bill; or, 8 two- dollar bills, and 3 three-dollar bills
... ; or, 5 two-dollar bills, and 5 three-dollar bills ; or, 2 two-dollar bills, and 7 three-dollar bills.
proof: 11X2+1X3=25.
8x2+3x3=25.
5X2+5x3=25.
2X2+7X3=25.
Ex. (7.) Let x = the bushels of corn, and y e= the bushels of wheat.
1. Then, by conditions, 70s+190y=920.
2. Dividing by 10, = 7a+19y=92.
3. Transposing, 7s=92— 19y.
4. Dividing, a:=13— 2y ^-£.
5. Changing terms, z=13 — 2y — z— — .
6. Substituting, n=-z— — .
7. Clearing of fractions, 7n=5y — 1.
8. Transposing, 5y=77i+l.


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