Linear system substitution: If 2x + 3y = 29 and y = x + 3, find the value of x.

Introduction / Context:This is a straightforward two-equation linear system where one equation already expresses y in terms of x. Substitution directly yields x.

Given Data / Assumptions:

• 2x + 3y = 29
• y = x + 3

Concept / Approach:Substitute y into the first equation and solve for x. Then y can be found if desired.

Step-by-Step Solution:2x + 3(x + 3) = 292x + 3x + 9 = 29 → 5x = 20 → x = 4

Verification / Alternative check:Then y = x + 3 = 7; check: 2*4 + 3*7 = 8 + 21 = 29, consistent.

Why Other Options Are Wrong:5, 6, 7, 8 do not satisfy the substituted equation 2x + 3(x + 3) = 29.

Common Pitfalls:Arithmetic slips in combining like terms or mis-substituting y.

Final Answer:4