Question

Which of the following systems of equations is an example of one where elimination is the best method?

a. y=3/8x+14, 2x-9y=-36
b. 2x+3y=18, -6x+y=12
c. y=1/4x+2, 3x-7y=42
d. x=4, y=-9

Answer 1

System (b) 2x+3y=18, -6x+y=12 is the best for the elimination method because it allows for easy elimination of x after multiplying the second equation by 3, combining the equations, and solving for y.

Step-by-step explanation:

When considering which system of equations is best suited for the elimination method, it's important to look for a situation where one can easily eliminate one of the variables by adding or subtracting the equations. The elimination method involves lining up two equations and finding a way to cancel out one of the variables by combining the equations. In the provided options, choice (b) 2x+3y=18, -6x+y=12 is ideal for the elimination method because you can multiply the second equation by 3 and then add it to the first equation to eliminate the x variable.

Multiply the second equation by 3 to get the system to 2x+3y=18, -18x+3y=36.

1. Add the two equations together to eliminate the x variable: (2x - 18x) + (3y + 3y) = 18 + 36.
2. After adding, you get -16x+6y=54.
3. Divide the entire equation by -2 to simplify: 8x-3y=-27.
4. Since the original first equation is 2x+3y=18, when we add the new equation 8x-3y=-27, the y variable is eliminated, and we're left with an equation that we can solve for x.

Using these steps, the elimination method for system (b) can be effectively employed to find the solution for x and then substituted back to find the solution for y.