Question

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

(2x + 3y = -5
2x - 3y = 10
Choose all answers that apply:
Add the equations.
Subtract the bottom equation from the top equation.
Multiply the top equation by 2. then add the equations.

Answer 1

• add the equations
• subtract the bottom equation from the top equation

Explanation:

The coefficients of the x-terms are 2 and 2, so subtracting one equation from the other will give an x-coefficient of 0, eliminating the x-terms. One might choose to subtract the bottom equation, as it is the one with the least y-coefficient. This strategy would result in a y-term with a positive coefficient:

(2x +3y) -(2x -3y) = (-5) -(10)

6y = -15 . . . . . . the result of subtracting the bottom equation

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The coefficients of the y-terms are 3 and -3, so adding the two equations will give a y-coefficient of 0, eliminating the y-terms.

(2x +3y) +(2x -3y) = (-5) +(10)

4x = 5 . . . . . . the result of adding the two equations.

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A variable could be eliminated by ...

• add the equations
• subtract the bottom equation from the top equation

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Additional comment

The third choice would give ...

2(2x +3y) +(2x -3y) = 2(-5) +(10)

6x +3y = 0 . . . . . . . . eliminates the constant. Both variables remain.