which equation can pair with $x + 2y = 5$ to create an inconsistent system?\n$2x + 4y = 3$\n$5x + 2y =…

Explanation:

Step1: Recall inconsistent system rule

An inconsistent linear system has equations where $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$ for $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$.

Step2: Test first option

For $x+2y=5$ and $2x+4y=3$: $\frac{1}{2}=\frac{2}{4}\neq\frac{5}{3}$

Step3: Verify other options fail

• $5x+2y=3$: $\frac{1}{5}\neq\frac{2}{2}$
• $6x+12y=30$: $\frac{1}{6}=\frac{2}{12}=\frac{5}{30}$ (dependent system)
• $3x+4y=8$: $\frac{1}{3}\neq\frac{2}{4}$

Answer:

A. $2x + 4y = 3$