In the system 2x + 3y = 12 and 5x + 4y = 23, which pair of multipliers clears x when the two rules are then added?

1. The x terms are 2x and 5x, and the smallest number both divide into is 10. 2. Multiplying the first rule by 5 turns 2x into 10x. 3. Multiplying the second rule by minus 2 turns 5x into minus 10x. 4. Adding then gives 10x minus 10x, which is zero, so x is gone. 5. The rest becomes 15y minus 8y equals 60 minus 46, so 7y = 14 and y = 2, giving x = 3. 6. Option A turns the x terms into 4x and minus 25x, which do not cancel. 7. Option D leaves 10x and 10x, so adding doubles x instead of clearing it. 8. Option C targets neither unknown cleanly, since it gives 8x and minus 15x. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_