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Which equation can be used to find two numbers such that twice the first equals three times the second and three times their difference exceeds twice the second by 13?
Wiki User
∙ 9y ago
Let the two numbers be x and y, then:
- Twice the first equals three times the second: 2x = 3y
- Three times their difference exceeds the second by 13: 3(x - y) = y + 13
From equation (1) it is clear the first number (x) is greater than the second (y), so their difference is x - y.
Equation (2) can be rearranged:
3(x - y) = y + 13
→ 3x - 3y = y + 13
→ 3x = 4y + 13
This gives two simultaneous equations:
- 2x - 3y = 0
- 3x - 4y = 13
which can then be solved to find the two numbers (x and y).
Wiki User
∙ 9y ago
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