a system of equations has infinitely many solutions. if 2y - 4x = 6 is one of the equations, which could be…

Explanation:

Step1: Rewrite the given equation

Rewrite $2y - 4x=6$ in slope - intercept form $y = mx + b$. Add $4x$ to both sides: $2y=4x + 6$. Then divide by 2, we get $y = 2x+3$.

Step2: Rewrite each option in slope - intercept form

• Option 1: $y = 2x+6$.
• Option 2: $y = 4x+6$.
• Option 3: Multiply $-y=-2x - 3$ by $- 1$, we get $y = 2x+3$.
• Option 4: Multiply $-y=-4x + 6$ by $-1$, we get $y = 4x-6$.

Step3: Determine the correct option

A system of linear equations has infinitely many solutions when the two equations represent the same line (same slope $m$ and same y - intercept $b$). The equation $y = 2x+3$ (from the given equation) and $y = 2x+3$ (from option 3) are the same line.

Answer:

$-y=-2x - 3$