Two numbers are such that their sum is 17 and the sum of twice the first number and…
MATHEMATICS · Multi-part · AoPS · Mathematics · Multi-Variable Linear Equations · Multi-Variable Linear Equations
Problem
Two numbers are such that their sum is 17 and the sum of twice the first number and thrice the second number is 46.
(i) Represent the above information as a pair of linear equations in two variables.
(ii) Solve the equations to find the two numbers.
(iii) The larger number is decreased by 3 and the smaller number is increased by 5. Form a new pair of equations representing this change and solve to verify that the results are consistent with the original solution.