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This question has two parts. First, answer Part A. Then, answer Part B.

Part A:
Consider the system.

[tex]\[
\begin{array}{l}
3x + 2y = 8 \\
9x - 12y = 6
\end{array}
\][/tex]

Which method(s) would you use to solve the system? Select all that apply.

A) Elimination using addition
B) Elimination using multiplication
C) Graphing
D) Substitution



Answer :

GinnyAnswer
To solve the system of equations:
[tex]\[ \begin{array}{l} 3x + 2y = 8 \\ 9x - 12y = 6 \end{array} \][/tex]

We analyze the feasibility of each method:

### A) Elimination using addition
This method could be successfully used if the equations can be formulated suitably to cancel out one variable when added.

### B) Elimination using multiplication
In this method, we may need to multiply one or both equations to align the coefficients of one of the variables for elimination. This is also a viable method for this system.

### C) Graphing
Graphing involves plotting the two equations on a graph to find their intersection point. This method can also be applied provided the equations can be graphically represented.

### D) Substitution
This method entails solving one of the equations for one variable and then substituting this expression into the other equation. This method can also be applied here.

Given these considerations, all four methods are applicable:
- Elimination using addition
- Elimination using multiplication
- Graphing
- Substitution

So, the methods to solve the system are: A, B, C, and D.

### Part A Answer:
A) elimination using addition
B) elimination using multiplication
C) graphing
D) substitution

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