Answer:
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).