Question

Which of these strategies would eliminate a variable in the system of equations?

{-7x + 2y = 5, 3x - 5y = -5}
A) Multiply the first equation by 3 and the second equation by -7, then add the equations.
B) Add the two equations together.
C) Subtract the second equation from the first equation.
D) Divide both equations by 5.

Answer 1

The strategy that eliminates a variable in a system of equations is to perform operations that result in the coefficients of one of the variables being additive inverses (having equal magnitude but opposite signs). This allows the variable to cancel out when the equations are combined.

The correct choice is:

A) Multiply the first equation by 3 and the second equation by -7, then add the equations.

By doing this, the coefficients of \(x\) in both equations will become additive inverses, and adding the equations will eliminate the \(x\)-terms.

Step-by-step explanation:

hope this will help you

Answer 2

The strategy that eliminates a variable in the given system of equations is A) Multiply the first equation by 3 and the second equation by -7, then add the equations. This strategy removes the variable x, leaving a single variable equation.

Step-by-step explanation:

To eliminate a variable in the system of equations {-7x + 2y = 5, 3x - 5y = -5}, we must manipulate the equations such that adding or subtracting them will result in one variable being canceled out. Let's evaluate the given strategies:

• A) Multiply the first equation by 3 and the second equation by -7, then add the equations. Multiplying the first equation by 3 gives us: -21x + 6y = 15. Multiplying the second equation by -7 gives us: -21x + 35y = 35. Adding these together: -21x + 6y + (-21x + 35y) = 15 + 35, which simplifies to: 41y = 50. This step eliminates x, leaving us with a single variable equation.
• B) Add the two equations together. This would be: (-7x + 2y) + (3x - 5y) = 5 - 5, which simplifies to -4x - 3y = 0. This does not eliminate any variable, since both x and y are still present.
• C) Subtract the second equation from the first equation. This gives us: (-7x + 2y) - (3x - 5y) = 5 - (-5), simplifying to -10x + 7y = 10. Again, no variable is eliminated.
• D) Divide both equations by 5. This action will not eliminate any variable, it will just simplify each equation.

Therefore, the correct strategy to eliminate a variable is A) Multiply the first equation by 3 and the second equation by -7, then add the equations.