Question

Which of these strategies would eliminate a variable in the system of equations? 2x + 3y = -5, 2x - 3y = 10

1) Add the equations
2) Subtract the bottom equation from the top equation
3) Multiply the top equation by 2, then add the equations

Answer 1

To eliminate a variable in a system of equations, you can add the equations, subtract one equation from another, or multiply an equation by a constant and add them. All three strategies can eliminate a variable successfully.

Step-by-step explanation:

To eliminate a variable in a system of equations, we need to perform operations that will result in one of the variables being eliminated. Let's analyze the three strategies:

1. Add the equations: If we add the two equations together, the variable 'x' will be eliminated because the coefficients will cancel each other out:
   
   (2x + 3y) + (2x - 3y) = (-5) + (10)
   
   4x = 5
   
   2x = 5/2
   
   x = 5/4
2. Subtract the bottom equation from the top equation: By subtracting the second equation from the first equation, the variable 'y' will be eliminated:
   
   (2x + 3y) - (2x - 3y) = (-5) - (10)
   
   6y = -15
   
   y = -15/6
   
   y = -5/2
3. Multiply the top equation by 2, then add the equations: By multiplying the first equation by 2 and adding the two equations together, the variable 'x' will be eliminated:
   
   (2x + 3y) + 2(2x - 3y) = (-5) + 2(10)
   
   (2x + 3y) + (4x - 6y) = (-5) + 20
   
   6x - 3y = 15
   
   6x = 15 + 3y
   
   6x = 15 - 3y
   
   x = (15 - 3y)/6

So, all three strategies can eliminate a variable from the system of equations.