If 3x + y = 5 and x - y = 3, then
2023
If 3x + y = 5 and x - y = 3, then
Answer: A. x = 2, y = -1 — ConceptSubstitution rewrites one equation to express one variable in terms of the other; inserting that expression into the remaining equation reduces the…
- A.
x = 2, y = -1
- B.
x = -2, y = -1
- C.
x = -2, y = 1
- D.
More than one of the above
- E.
None of the above
Show answer & explanation
Correct answer: A
Concept
Substitution rewrites one equation to express one variable in terms of the other; inserting that expression into the remaining equation reduces the system to one variable. A pair solves the system only when the same values satisfy every equation.
Application
From x - y = 3, write y = x - 3.
Substitute y = x - 3 into 3x + y = 5: 3x + (x - 3) = 5.
Combine like terms: 4x - 3 = 5, so 4x = 8 and x = 2.
Use y = x - 3: y = 2 - 3 = -1.
Cross-check
Substitution gives 3(2) + (-1) = 5 and 2 - (-1) = 3, so the pair satisfies both original equations.
Therefore, x = 2 and y = -1.