Asystem of equations has 1 solution. if 4x – y = 5 is one of the equations, which could be the other equation?

y = –4x + 5
y = 4x – 5
2y = 8x – 10
–2y = –8x – 10

A system of linear equations will have one solution if the equations making up the system is linearly independent (i.e. the equations are not formed by multiplying any of the equation with a common factor) and the line formed by the equation are not parallel (i.e. does not have the same slope or does not have the same x-value when y is made subject of formular) Given that one of the equations is 4x - y = 5 which can be rewritten as y = 4x - 5. Multiplying through by 2, gives: 2y = 8x - 10. For the equation: -2y = -8x - 10, making y the subject of the formular gives -2y/-2 = -8x/-2 - 10/-2 giving y = 4x + 10 which gives the same slope as the original equation. Thus the only equation which is not a multiple of the original equation or parallel to the original equation is y = -4x + 5 Therefore, the correct answer to the question "A system of equations has 1 solution. If 4x – y = 5 is one of the equations, which could be the other equation?" is y = -4x + 5.