# `.25x = .1 + .2y` Write each equation in standard form. Identify A, B and C

### Textbook Question

Chapter 2, 2.2 - Problem 38 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
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taangerine | Student, Grade 12 | (Level 1) Valedictorian

Posted on

To add on to Wiggin42's answer (which is correct), I would like to take the time to explain the reason why this TA got this answer. In addition to the the given standard form formula:

Ax+By=C

There are also 3 rules that should be followed accordingly:

1. A shouldn't be negative.

2. A and B shouldn't both be zero.

3. And, A, B, and C should be integers.

#1 explains why the B integer is negative rather than the A integer. A can never be negative.

And, #3 explains the reason why the TA multiplied both sides of the equation by 20, they were not whole numbers. The original equation was written in decimal form. The TA found a common multiple that would eliminate the decimals (which was 20), and give us an integer. And, an integer is defined as a whole number.

Examples of an integer would be -2, -1, 0, 1, 2, etc.

Sources:

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

Standard form is given by the formula:

Ax + By = C

where A, B, C are constant integers.

Multiply by 20 to get:

5x = 2 + 4y

Rearrange to get:

5x - 4y = 2

Therefore, A = 5, B = -4, C = 2

Sources: