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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Middle/High School Algebra, Geometry, and Statistics (AGS)
1.22 Solving Equations - Substitution Method II

Example:
Solve 1/x + 1/y = 10 and 3/x + 2/y = 24.

Solution:
Given that 1/x + 1/y = 10 -----(1)
3/x + 2/y = 24---------(2)
Let 1/x = a and 1/y = b
The given equations can be written as
a + b = 10 --------(3)
3a + 2b = 24 --------(4)
Multiply the equation (3) by 2, we get
2a + 2b = 20--------(5)
Subtract (5) from (4)
3a + 2b = 24 --------(4)
2a + 2b = 20--------(5)
Subtract (5) from (4) we get

a = 4

Substitute a = 4 in equation (3), we get
4 + b = 10
b = 10 - 4
b = 6
but
a = 1/x = 4
x = 1/4
b = 1/y = 6
y = 1/6
Therefore, solution set {(1/4,1/6)}.


Directions: Choose the correct answer. Also write at least ten examples of your own.
Q 1: Solve 5/x + 2/y = 24 and 1/x + 3/y = 10.
x = 1/2 and y = 1/4
x = 1/4 and y = 1/2
x = 2 and y = 4
x = 4 and y = 2

Q 2: Solve 1/x + 3/y = 10 and 3/x + 2/y = 9.
x = 3 and y = 1
x = 1 and y = 1/3
x = 1/3 and y = 1
x = 1 and y = 3

Q 3: Solve 1/x + 3/y = 7 and 3/x + 4/y = 11.
x = 1 and y = 1/2
x = 2 and y = 1
x = 1 and y = 2
x = 1/2 and y = 1

Q 4: Solve 1/x + 1/y = 9 and 3/x + 2/y = 22.
x = 4 and y = 5
x = 5 and y = 4
x = 1/4 and y = 1/5
x = 1/5 and y = 1/4

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Question 6: This question is available to subscribers only!


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