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Verify Solutions

To verify that certain values are solutions to the given equation, we simply substitute them in and check. This is very similar to Trial and Error.

How many of the following pairs of integers are solutions to \( 2x + 3y = 20 \)? \[ (2, 3), (3, 5), (4, 4), (6, 3), (10, 0) \]

A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Trying the first option, \( 2 \times 2 + 3 \times 3 = 4 + 9 = 13 \neq 20 \).
Trying the second option, \( 2 \times 3 + 3 \times 5 = 6 + 15 = 21 \neq 20 \).
Trying the third option, \( 2 \times 4 + 3 \times 4 = 8 + 12 = 20 \). This is a solution.
Trying the fourth option, \( 2 \times 6 + 3 \times 3 = 12 + 9 = 21 \neq 20 \).
Trying the fifth option, \( 2 \times 10 + 3 \times 0 = 20 + 0 = 20 \). This is a solution.
Thus, 2 of the pairs are solutions.

Note by Arron Kau
3 years, 5 months ago

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2x+y=z,3x-y=0

Shrushti Lomte - 3 years, 4 months ago

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