Question

muriel’s equation
muriel says she has written a system of two linear equations that has an infinite number of solutions. one of the equations of the system is ( 3y = 2x - 9 ). which could be the other equation?
( \bigcirc ) ( 2y = x - 4.5 )
( \bigcirc ) ( y = \frac{2}{3}x - 3 )
( \bigcirc ) ( 6y = 6x - 27 )
( \bigcirc ) ( y = \frac{3}{2}x - 4.5 )

Explanation:

Step1: Rewrite given equation in slope-intercept form

Start with $3y=2x-9$. Divide all terms by 3:
$$y=\frac{2}{3}x-3$$

Step2: Identify condition for infinite solutions

A system of linear equations has infinite solutions if the equations are identical (same slope and y-intercept). We check each option to see if it matches $y=\frac{2}{3}x-3$.

• Option1: $2y=x-4.5$ → $y=\frac{1}{2}x-2.25$ (different slope/intercept)
• Option2: $y=\frac{2}{3}x-3$ (matches exactly)
• Option3: $6y=6x-27$ → $y=x-4.5$ (different slope/intercept)
• Option4: $y=\frac{3}{2}x-4.5$ (different slope/intercept)

Answer:

B. $y=\frac{2}{3}x-3$