Answer:
To eliminate a variable, you need to choose a strategy that allows you to add or subtract the equations in such a way that one variable will be eliminated. Let's go through the given options to determine the correct strategy:
A. Multiply the first equation by 2. Then add the equations.
If you multiply the first equation by 2, you get 10x + 6y = 8. If you add this equation to the second equation, you will not be able to eliminate either variable, as the coefficients of x and y do not match.
B. Multiply the first equation by 5 and the second equation by 2. Then add the equations.
If you multiply the first equation by 5, you get 25x + 15y = 20. If you multiply the second equation by 2, you get -4x - 16y = 12. Adding these equations gives you 21x - y = 32. This strategy allows you to eliminate y.
C. Multiply the second equation by 5. Then add the equations.
If you multiply the second equation by 5, you get -10x - 40y = 30. If you add this equation to the first equation, you will not be able to eliminate either variable, as the coefficients of x and y do not match.
D. Multiply the first equation by 2 and the second equation by 5. Then add the equations.
If you multiply the first equation by 2, you get 10x + 6y = 8. If you multiply the second equation by 5, you get -10x - 40y = 30. Adding these equations gives you -34y = 38. This strategy allows you to eliminate x.
Based on the options given, the correct strategy to eliminate a variable in this system of equations is: B.) Multiply the first equation by 5 and the second equation by 2. Then add the equations.