Question

a system of equations has infinitely many solutions. if 2y – 4x = 6 is one of the equations, which could be the other equation? y = 2x 6 y = 4x 6 –y = –2x – 3 –y = –4x 6

Answer 1

A system of equations has infinitely many solutions when the two lines representing the equations coincide. i.e. the two equations are the same or a multiple of each other.
2y - 4x = 6
2y = 4x + 6
2y = 2(2x + 3)
y = 2x + 3
-y = -(2x + 3)
-y = -2x - 3
Hence the other equation is -y = -2x - 3

Answer 2

If 2y – 4x = 6 is one of the equations, the second equation could be -y = -2x - 3

How to determine the equation?

The equation is give as:

2y - 4x = 6

For a system of equation to have infinitely many solutions, the equations in the system must be equivalent.

We have:

2y - 4x = 6

Add 4x to both sides

2y = 4x + 6

Divide through by -2

-y = -2x - 3

Hence, the second equation could be -y = -2x - 3

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