Question

y=–6x 2 –12x – 2y=–4 how many solutions does this linear system have?

Answer 1

For a linear system of equations, there can only be zero solution, 1 solution or an infinite number of solutions. Two lines cannot intersect more than once. The intersection of the lines is called the solution. For this case there could is no solution because it only shows one equation. It cannot intersect on its own line.

Answer 2

y = -6x + 2 . . . . . . . . equation (1)

-12x - 2y = -4 . . . . . . equation (2)

substitute  (1) into (2),

-12x - 2(-6x + 2) = -4

-12x + 12x - 4 = -4

-4 = -4

Both sides are same. If we arrive at a statement that is true, then the system has infinite number of solution.

So there are infinite number of solutions for system of equations

y=-6x + 2 and -12x - 2y=-4