Question

Refer to the system of linear equations shown below. Which of the following statements gives the best choice for multiplying to solve this system using the elimination method?

3x−6y=4
6x+11y=−2
1. Multiply the first equation by −11
and the second equation by 6
so the y-variables are eliminated.
2. Multiply the second equation by 1/2
so the x-variables are eliminated.
3. Multiply the first equation by −2
so the x-variables are eliminated.
4. Multiply the first equation by 2
so the x-variables are eliminated.

Answer 1

3: Multiplying the first equation by −2 so the x-variables are eliminated.

Explanation:

The elimination method is a strategy to solve a system of linear equations by eliminating one of the variables (usually the y variable) by adding or subtracting the equations. This can be done by multiplying one or both of the equations so that when added or subtracted, the y variable will cancel out.

In this case, the best option for multiplying to solve the system using the elimination method is to multiply the first equation by -2 so that the x-variables are eliminated. This is because when the first equation is multiplied by -2, it becomes -6x + 12y = 8, which has the same coefficient for x as the second equation. When the two equations are added, the x variable will cancel out, leaving us with an equation in terms of y, which can then be solved for x.

The equation after the elimination will look like this:

-6x + 12y + 6x + 11y = -2 + 8

6y = 6

y = 1

Finally, we can use this value of y to solve for x in one of the original equations:

3x - 6(1) = 4

3x = 10

x = 10/3 = 3.33

So the solution to the system is (3.33, 1).