Question

the movement of the progress bar may be uneven because questions can be worth more or less (including
which of the following systems has equations that are dependent?
$\bigcirc x+y=3$
$\bigcirc x-y=1$
$\bigcirc x=2$
$\bigcirc 2x=4$
$\bigcirc y=3x+4$
$\bigcirc y=3x-4$
$\bigcirc y=-2x+3$
$\bigcirc y=-2x-3$

Explanation:

Step1: Define dependent equations

Dependent equations are scalar multiples of each other, representing the same line.

Step2: Analyze each option

• First option: $x+y=3$ and $x-y=1$ are not scalar multiples.
• Second option: $x=2$ and $2x=4$ (rewrite $2x=4$ as $x=2$), so $2x=4 = 2\times(x=2)$. They are scalar multiples.
• Third option: $y=3x+4$ and $y=3x-4$ differ only by the constant term, not scalar multiples.
• Fourth option: $y=-2x+3$ and $y=-2x-3$ differ only by the constant term, not scalar multiples.

Answer:

$\boldsymbol{x=2}$ and $\boldsymbol{2x=4}$