Choose a method that can be used to solve the system of equations by elimination.
2x - 2y = 24
4x + 7y=-40
A. Subtract 2x from both equations and solve the first equation for y.
B. Multiply the first equation by -2 and add the second equation.
C. Add the first equation to the second equation and subtract 6x from both sides of the equation.
D. Subtract 7y from the second equation and add the first equation.
B. Multiply the first equation by -2 and add the second equation.
To solve a system of equations by elimination, you want to add or subtract the equations in a way that cancels out one of the variables.
Let's go through each option and see which one follows this approach:
A. Subtracting 2x from both equations and solving the first equation for y does not eliminate any variables.
B. Multiplying the first equation by -2 and adding the second equation is a valid strategy. This will eliminate the x variable when you add the two equations.
C. Adding the first equation to the second equation and subtracting 6x from both sides of the equation does not eliminate any variables.
D. Subtracting 7y from the second equation and adding the first equation is a valid strategy. This will eliminate the y variable when you add the two equations.
Therefore, the correct answer is option D.