In the system x + 3y = 11 and 2x - y = 8, by what number should the first rule be multiplied so that adding the two rules removes x?

1. The x terms are 1x in the first rule and 2x in the second. 2. For the two to cancel on adding, the first must become minus 2x. 3. Multiplying 1x by minus 2 gives minus 2x, so minus 2 is the multiplier. 4. The whole rule must be multiplied, giving minus 2x minus 6y equals minus 22. 5. Adding that to 2x minus y equals 8 leaves minus 7y equals minus 14, so y = 2 and then x = 5. 6. Multiplying by positive 2 would give 2x in both rules, so adding would double x rather than remove it. 7. Multipliers of 3 or minus 3 leave the x terms mismatched, so nothing cancels. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_