SOLUTION: are the two equations -6 + y = 2x and 2y - 4x = 12 dependent? A. No, because they are not parallel B. Yes, because they have the same graph C. Yes, because both are the equ

Question 1018235: are the two equations -6 + y = 2x and 2y - 4x = 12 dependent?

A. No, because they are not parallel
B. Yes, because they have the same graph
C. Yes, because both are the equations of straight lines
D. No, because the equations are not written the same
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's a reference on type of systems of equations.

http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson

the equations you have are dependent because they are equivalent to each other and therefore would generate the same line on the graph.

this means there are an infinite number of possible solutions that are common to both equations.

the best answer that fits is selection B.

the 2 equations are:

-6 + y = 2x and 2y - 4x = 12

solve for y in the first equation to get y = 2x + 6.

solve for y in the second equaiton to get y = 2x + 6.

the equations are identical.

they have the same slope and the same y-intercept.

they're equivalent.

they fit the definition of dependent equations.

dependent equations are defined as:

here's another link that gives a definition of dependent equations.

http://hotmath.com/hotmath_help/topics/consistent-and-dependent-systems.html

Answer by ikleyn(52907) (Show Source): You can put this solution on YOUR website!
.
are the two equations -6 + y = 2x and 2y - 4x = 12 dependent?

A. No, because they are not parallel
B. Yes, because they have the same graph
C. Yes, because both are the equations of straight lines
D. No, because the equations are not written the same
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See also the lesson Geometric interpretation of the linear system of two equations in two unknowns in this site.

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