Graph each system of equations and describe it as consistent and independent, consistent and dependent, inconsistent, or none of these. 9x-6y=1 3x-2y=21

Question

a. consistent and dependent 

b. consistent and independent

d. none of these

c. inconsistent

Answer 1

• A system of equations is consistent if it has at least one solution. Graphically, this means that the graphs of the equations in the system overlap or intersect somewhere.

- If the two equations intersect at a single point, then they are independent. There is only one solution.

- If the two graphs overlap completely, the system is are dependent. There are many solutions.

An example of a dependent system would be the equations x+y=1 and 2x+2y=2 as the second equation is the first multiplied by 2. The graphs are exactly the same line.

 

• If the graphs do not intersect anywhere, the system is inconsistent, and there is no solution. The most common case for this is two parallel lines.