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Middle/High School Algebra, Geometry, and Statistics (AGS)
1.23 Dependent Equations

Dependent equations are consistent with many solutions.

Example: two lines that coincide infinitely many points has many solutions.

The equation ax + by + c = 0 is multiplied by a constant k, the resulting equation is kax + kby + kc = 0.
The equation ax + by + c = 0 and kax + kby + kc = 0.are known as dependent equations.

Example:
If 3x + 2y + 3 = 0 and constant 2, write the dependent equation.
solution:
Multiply the given equation with the given constant term, we get the dependent equation.
2(3x + 2y + 3 = 0) = 6x+ 4y + 6 = 0.

Directions: Choose the correct answer. Also write at least ten examples of your own.
Q 1: If 2x + 3y + c = 0 and constant 3
6x+9y+c = 0
6x+9y+3c = 0
6x+3y+3c = 0
2x+9y+3c = 0

 Q 2: If 2x + 5y + c = 0 and constant 6
2x+30y+6c=0
12x+5y+6c=0
12x+30y+6c=0
12x+30y+c=0

Q 3: If 3x + 5y + c = 0 and constant 7
3x+35y+7c=0
21x+35y+c=0
21x+5y+7c=0
21x+35y+7c=0

 Q 4: If x + 7y + c = 0 and constant 3
3x+21y+c=0
3x+21y+3c=0
x+21y+3c=0
3x+3y+3c=0

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 Question 6: This question is available to subscribers only!


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