Solve this system by adding the rules: 4x + y = 19 and 4x - 3y = 7.

1. Both rules carry 4x, so multiply the second rule by minus 1 to get minus 4x + 3y = -7. 2. Add that to the first rule: the x terms cancel and y + 3y gives 4y. 3. On the right, 19 plus minus 7 gives 12, so 4y = 12 and y = 3. 4. Put y = 3 into the first rule: 4x + 3 = 19, so 4x = 16 and x = 4. 5. Check in the second rule: 4 times 4 is 16, 3 times 3 is 9, and 16 minus 9 is 7. 6. Option C fits the first rule only, since 4 times 5 minus 3 times minus 1 is 23 rather than 7. 7. Option D also fits the first rule only, since 8 minus 33 is minus 25 rather than 7. 8. Option A swaps the two values, which fails both rules at once. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_