a system of equations has no solution. if ( y = 8x + 7 ) is one of the equations, which could be the other…

a system of equations has no solution. if ( y = 8x + 7 ) is one of the equations, which could be the other equation?\n( 2y = 16x + 14 )\n( y = 8x - 7 )\n( y = -8x + 7 )\n( 2y = -16x - 14 )

a system of equations has no solution. if ( y = 8x + 7 ) is one of the equations, which could be the other equation?\n( 2y = 16x + 14 )\n( y = 8x - 7 )\n( y = -8x + 7 )\n( 2y = -16x - 14 )

Answer

Explanation:

Step1: Recall the condition for no - solution

A system of linear equations (y = m_1x + c_1) and (y=m_2x + c_2) has no solution when (m_1=m_2) and (c_1\neq c_2) (parallel lines).

Step2: Analyze each option

  • Option 1: For (y = 8x+7) and (2y = 16x + 14) (rewrite as (y = 8x+7)), (m_1 = 8,m_2 = 8) and (c_1=7,c_2 = 7). The lines are coincident (infinite solutions).
  • Option 2: For (y = 8x+7) and (y = 8x - 7), (m_1=8,m_2 = 8) and (c_1 = 7,c_2=-7). Since (m_1=m_2) and (c_1\neq c_2), the lines are parallel (no solution).
  • Option 3: For (y = 8x+7) and (y=-8x + 7), (m_1 = 8,m_2=-8). The lines intersect (unique solution).
  • Option 4: For (y = 8x+7) and (2y=-16x - 14) (rewrite as (y=-8x - 7)), (m_1 = 8,m_2=-8). The lines intersect (unique solution).

Answer:

(y = 8x-7)