Solve a pair of linear equations: Twice the first number plus thrice the second equals 100, and thrice the first plus twice the second equals 120. Which is the larger number?

Introduction / Context:
This is a direct two-equation, two-unknowns problem. Solve the linear system to find both numbers, then identify the larger one. Elimination using aligned coefficients makes the arithmetic quick and clean.

Given Data / Assumptions:

• 2x + 3y = 100
• 3x + 2y = 120

Concept / Approach:
Eliminate one variable by forming equal coefficients on x or y. Subtract the resulting equations to find the other variable, then back-substitute to get the first. Compare the values to decide which is larger.

Step-by-Step Solution:

Verification / Alternative check:
Check in the first equation: 2*32 + 3*12 = 64 + 36 = 100 ✔; second: 3*32 + 2*12 = 96 + 24 = 120 ✔.

Why Other Options Are Wrong:
12 and 14 are the smaller or unrelated values; 35 and 28 do not satisfy both equations simultaneously.

Common Pitfalls:
Arithmetic slips when scaling equations or subtracting can flip signs and produce wrong values; always verify in both original equations.

Final Answer:
32