Question

Part 2: For each system of equations in this section, state which method (table, graph, substitution, elimination) is appropriate for solving each system. Be sure to explain thoroughly, provide justif cation from the equations for your choice. System of equations Explain and Justify which method is appropriate 3x + 8y =-4 2x – 4y = 16 6x - y = 16 x = 4y - 5 x + y = 19 3x - 2y =-3

Answer 1

Any system of equations can be solved for any of those methods. Generally, using a graph and using a table require a lot of work, since it is not always easy to read the coordinates on a graph (specially when dealing with fractionary solutions), and on a table the issue is the same as with the graphs.

Usually, elimination and substitution methods are used depending on the coefficients of the variables on the system. Whenever there is a coefficient of 1 on some variable, the elimination method can be used very easily. Whenever there is already an isolated variable, the substitution method is prefered.

For the system:

`\begin{gathered} 3x+8y=-4 \\ 2x-4y=16 \end{gathered}`

If we multiply the second equation by 2, we get:

`\begin{gathered} 2(2x-4y)=2(16) \\ \Rightarrow4x-8y=32 \end{gathered}`

So the system can be rewritten as:

`\begin{gathered} 3x+8y=-4 \\ 4x-8y=32 \end{gathered}`

Since the coefficient of y is +8 in one equation and -8 in the other, we can use the elimination method by adding both equations side by side.

For the system:

`\begin{gathered} 6x-y=16 \\ x=4y-5 \end{gathered}`

The second equation has already an isolated variable, x. Then, we can use the substitution method by plugging in the expression for x in the first equation.

For the system:

`\begin{gathered} x+y=19 \\ 3x-2y=-3 \end{gathered}`

Since x and y have a coefficient of 1, we can multiply the first equation by 2, so the variable y would get a coefficient of 2, which will help us apply the elimination method, so when adding both equations, +2y and -2y cancell out.