Question

Part 1 : When solving systems of equations, how do you determine what method to use?

Part 2 : Choose 1 system of equations from the choices below. Then, solve the system and post your solution, showing your steps so that other students can see which method you chose.

–y + 3x = 6
y = –6x + 12


6x – 4y = 54
–9x + 2y = –69


2y = x + 1
–2x – y = 7
...?

Answer 1

To solve systems of equations, select a method based on the system's setup; using substitution, we solve the given system and find the solution to be (2, 0).

Step-by-step explanation:

When solving systems of equations, one must choose the method that best fits the problem's constraints. Methods include substitution, elimination, and graphing. The method selected often depends on how the equations are presented and which method allows for the most straightforward calculation.

Choosing the system –y + 3x = 6 and y = –6x + 12, we can solve it using substitution since the second equation is already solved for y:

1. Substitute the expression for y from the second equation into the first.
2. So –(–6x + 12) + 3x = 6.
3. Simplify to get 6x – 12 + 3x = 6.
4. Combine like terms to get 9x – 12 = 6.
5. Add 12 to both sides to get 9x = 18.
6. Divide by 9 to find x = 2.
7. Plug x back into the second equation to get y = –6(2) + 12, hence y = 0.

Our solution is (x, y) = (2, 0).

Answer 2

Part 1. The selection of method to use for solving system of equations is a matter of arbitrary choice. That is, what's convenient for you. For me, elimination is easier.
Part 2. I'll try solving the second system.6x-4y = 54-9x+2y = -69
Multiplying the first equation by 9 and the second equation by 6.
54x - 36y = 486-54x + 12y = -414
Adding the two equations,
-24y = 72y = -3
Subtitute back to one of the equations,-9x + 2y = -69-9x + 2(-3) = -6969 - 6 = 9x9x = 63x = 7
The solution is then (7, -3).