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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 3x + 2y - 5 = 0 and constant 3
9x+6y+15=0
9x+6y-5=0
9x+6y-15=0
9x+3y-15=0

Q 2: If 3x + 5y + c = 0 and constant 7
21x+5y+7c=0
21x+35y+7c=0
3x+35y+7c=0
21x+35y+c=0

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

Q 4: If 2x + 4y - c = 0 and constant 2
4x+4y-2c=0
4x+8y+2c=0
2x+8y-2c=0
4x+8y-2c=0

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Question 6: This question is available to subscribers only!


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