SOLUTION: Please help me solve this equation: A. Determine the type of system (inconsistent, consistent and independent, consistent and dependent) using algebraic methods and state the num

Question 1171442: Please help me solve this equation:
A. Determine the type of system (inconsistent, consistent and independent, consistent and dependent) using algebraic methods and state the number of solutions.
B. Solve each system graphically and give the solution/s (if coinciding, give 2) and verify.
C. Solve each system by using substitution method.
D. Solve each system by using elimination method.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the equations are consistent and dependent.
this means they are identical and make the same graph.
here's a graph of the equations.

as you can see, they make the same line on the graph.
that's because the equations are identical.

to solve this system of equations by the substitution method, do the following:
2x + 4y = 8
6x + 12y = 24
solve for y in the first eqution to get:
y = (8-2x)/4
simplify to get:
y = 2 - .5x
replace y with 2 - .5x in the second equation to get:
6x + 12 * (2 - .5x) = 24
simplify to get:
6x + 42 - 6x = 24
combine like terms to get 24 = 24.
since the variables disappeared and the equation is true, then you have a consistent and dependent solution, meaning the equations are identical.

to solve this system of equations by the elimination method, do the following:
2x + 4y = 8
6x + 12y = 24
multiply both sides of the first equation by 3 and leave the second equation as is to get:
6x + 12y = 24
6x + 12y = 24
subtract the second equation from the first to get:
0 + 0 = 0
since the variables disappeared and the equation is still true, you have identical equations.

here's a reference.
https://www.jamesbrennan.org/algebra/systems/solution_set.htm

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