Julia wrote a linear equation in standard form as –6x – 3y = 10. Arthur noticed that the equation was not written in standard form and wants to tell Julia how to fix it. What advice should he give her?

In standard form, Ax + By = C, the coefficients A and B should be integers with no common factor greater than 1, and A is usually written positive. In –6x – 3y = 10, the coefficients have no common factor greater than 1 because 10 is not divisible by 3. Multiplying both sides by –1 gives 6x + 3y = –10, making A positive without changing the equation’s solutions. Thus, Arthur should advise Julia to multiply both sides by –1.

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