a system of equations has 1 solution. if (4x - y = 5) is one of the equations, which could be the other…

a system of equations has 1 solution. if (4x - y = 5) is one of the equations, which could be the other equation?\n(y=-4x + 5)\n(y = 4x - 5)\n(2y = 8x - 10)\n(-2y=-8x - 10)

a system of equations has 1 solution. if (4x - y = 5) is one of the equations, which could be the other equation?\n(y=-4x + 5)\n(y = 4x - 5)\n(2y = 8x - 10)\n(-2y=-8x - 10)

Answer

Explanation:

Step1: Rewrite the given equation in slope - intercept form

Given (4x - y=5), rewrite it as (y = 4x-5). The slope (m = 4) and the (y) - intercept (b=-5). For a system of linear equations (y = m_1x + b_1) and (y=m_2x + b_2) to have exactly one solution, (m_1\neq m_2).

Step2: Analyze each option

  • Option 1: (y=-4x + 5) Here (m=-4\neq4).
  • Option 2: (y = 4x-5) Here (m = 4) and (b=-5). The two equations (y = 4x-5) (from the given (4x - y=5)) and (y = 4x-5) are the same line (infinite solutions).
  • Option 3: (2y=8x - 10) Divide by (2): (y = 4x-5). Same as the line (y = 4x - 5) (infinite solutions).
  • Option 4: (-2y=-8x - 10) Divide by (- 2): (y = 4x + 5). Here (m = 4). The two lines (y=4x-5) (from (4x - y = 5)) and (y = 4x + 5) are parallel ((m_1=m_2 = 4)) (no solution).

Answer:

A. (y=-4x + 5)