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

a system of equations has infinitely many solutions. if ( 2y - 4x = 6 ) is one of the equations, which could be the other equation?\n( y = 2x + 6 )\n( y = 4x + 6 )\n( -y = -2x - 3 )\n( -y = -4x + 6 )

a system of equations has infinitely many solutions. if ( 2y - 4x = 6 ) is one of the equations, which could be the other equation?\n( y = 2x + 6 )\n( y = 4x + 6 )\n( -y = -2x - 3 )\n( -y = -4x + 6 )

Answer

Explanation:

Step1: Simplify the given equation

Given (2y - 4x=6). Divide each term by (2): (y - 2x = 3), which can be rewritten as (y=2x + 3) or (-y=-2x - 3) (multiply both sides by (- 1)).

Step2: Check each option

  • For (y = 2x+6): The slope is (2) (same as (y = 2x + 3)), but the (y)-intercepts ((6) vs (3)) are different. So, parallel lines (no solution).
  • For (y = 4x+6): The slope ((4)) is different from (2). So, intersecting lines (one - solution).
  • For (-y=-2x - 3): Multiply both sides by (-1) gives (y = 2x+3), which is the same as the simplified form of the given equation. So, coinciding lines (infinitely many solutions).
  • For (-y=-4x + 6): Multiply both sides by (-1) gives (y = 4x-6). The slope ((4)) is different from (2). So, intersecting lines (one - solution).

Answer:

(\boxed{-y=-2x - 3})