Solve the System by Elimination $\begin{array} { l } \frac { x + 4 } { 5 } + \frac { 2 y - x } { 10 } = 2 \\\frac { x + 2 } { 4 } + \frac { 3 y + 4 } { 5 } = - 3\end{array}$

question 181

Multiple Choice

Solve the system by elimination.
$\begin{array} { l } \frac { x + 4 } { 5 } + \frac { 2 y - x } { 10 } = 2 \\\frac { x + 2 } { 4 } + \frac { 3 y + 4 } { 5 } = - 3\end{array}$

• A) \(\{ ( 158 , - 73 ) \}\)
• B) \(\phi\)
• C) \(\{ ( - 14,13 ) \}\)
• D) \(\{ ( - 73,158 ) \}\)

---

Definitions:

Hypothetical

Based on or serving as a hypothesis, a supposed but unproven premise or supposition used as the basis for further reasoning.

Disjunctive

A logical term referring to a choice between alternatives, often expressed in the format "A or B".

Syllogism

A form of logical reasoning where a conclusion is drawn from two given or assumed propositions (premises), each sharing a common or middle term not present in the conclusion.

Hypothetical Syllogism

A form of logical argument where two conditional statements lead to a conclusion, if P then Q; if Q then R; therefore, if P then R.