3. What would be the simplest way to solve the system?

y=1/2x
2x + 3y = 28

A. Graphing
B. Substitution***** MY ANSWER!
C. Elimination
D. Distributive

4. What is the solution of the system?
y=-3x
2x + 3y = 6

A. (2,6)
B. (-1,3)
C. (-2,6)*****MY ANSWER!
D. (1.5, -4.5)

Please help, and if you have any other answers, please tell me! :)

John1 meant to say 3(-3x) = -9x , not -6x

then 2x - 9x = 6
-7x = 6
x = -6/7 ---> not found in any of the answers, so I suspect a typo somewhere
y = -3(-6/7) = 18/7

(-6/6 , 18/7) is the correct solution

This answer works in both equations

You'll are all wrong!!! The correct answer to #7 is (B.) Substitution and the correct answer to #8 are (C.) (-2,6).

And Reiny... you didn't make any sense and the "answer" you gave wasn't even an option.

To solve the first system of equations, y = 1/2x and 2x + 3y = 28, you correctly chose the simpliest method, which is Substitution. Here's how you can use Substitution to solve the system:

1. Start with the first equation, y = 1/2x.
2. Substitute the value of y from the first equation into the second equation.
- Replace y in the second equation with 1/2x.
- The second equation becomes 2x + 3(1/2x) = 28.
3. Simplify the equation.
- Distribute 3 to (1/2x). The equation becomes 2x + (3/2)x = 28.
- Common denominator. Rewrite (3/2)x as (6/4)x. The equation becomes 2x + (6/4)x = 28.
- Combine like terms. (2 + 6/4)x = 28. Simplify to (14/4)x = 28.
- Divide both sides of the equation by (14/4) to isolate x. The equation becomes x = (28)/(14/4).
- Simplify the right side. x = 8.
4. Now that you have the value of x, substitute it back into one of the original equations to find y.
- Use the first equation, y = 1/2x. Substitute x = 8.
- y = 1/2(8) = 4.
5. Therefore, the solution to the system of equations is x = 8 and y = 4.

For the second system of equations, y = -3x and 2x + 3y = 6, you chose the solution C.(-2,6). However, that is not the correct solution. Let's use the Substitution method to find the correct solution:

1. Start with the first equation, y = -3x.
2. Substitute the value of y from the first equation into the second equation.
- Replace y in the second equation with -3x.
- The second equation becomes 2x + 3(-3x) = 6.
3. Simplify the equation.
- Distribute 3 to (-3x). The equation becomes 2x - 9x = 6.
- Combine like terms. (-7x) = 6.
- Divide both sides of the equation by (-7) to isolate x. The equation becomes x = -(6/7).
- Simplify the right side. x = -6/7.
4. Now that you have the value of x, substitute it back into one of the original equations to find y.
- Use the first equation, y = -3x. Substitute x = -6/7.
- y = -3(-6/7) = 18/7 = 2 4/7.
5. Therefore, the correct solution to the system of equations is x = -6/7 and y = 2 4/7.

I hope this helps clarify the solutions to both systems of equations. If you have any other questions, feel free to ask!

3) probably because it is set up for substitution.

C works in the first equation, but check it in the second equation. I don't think it works there.

2x + 3(-3x) = 6
2x -6x = 6
can you finish if from here. make sure the answer works in both equations.