SOLUTION: 1. Given the following equation: x-2y=6 Create one equation for each of the following: An equation of a line that is CONSISTENT with the given equation. An equation of a lin

Question 400509: 1. Given the following equation: x-2y=6
Create one equation for each of the following:
An equation of a line that is CONSISTENT with the given equation.
An equation of a line that is INCONSISTENT with the given equation.
An equation of a line that is DEPENDENT with the given equation.
You CANNOT use the numbers in the given equation as part of your answers.
EXPLAIN how you know your answers are correct.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you multiply the coefficient on one of the variables by some factor and multiply the other variable's coefficient and the constant by some different factor, you will create a consistent and independent equation.

If you multiply the coefficient on each of the variables by the same factor but multiply the constant by some different factor, you will create an inconsistent equation.

If you multiply the two coefficients on the variables AND the constant all by the same factor, you will create a consistent and dependent equation.

Changing one of the variable coefficients relative to the other changes the slope. If lines have different slopes, they must intersect, hence consistent AND independent. If you alter both coefficients by the same factor, you keep the same slope but altering the constant by a different factor changes the intercept. The lines are then parallel, hence inconsistent. If you change all of the coefficients and the constant by the same factor, you keep the same slope and intercept, hence a consistent and dependent system.

John

My calculator said it, I believe it, that settles it

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