Question

One equation in a linear system of two equations is 3x - 2y = 8. the system has an infinite number of solutions. which could be the other equation of this linear system?

Answer 1

The equation 3x - 2y = 8 and 6x - 4y = 16 are systems of equations with infinite solutions.

A linear system of equations can have (a)unique solutions, (b) infinite number of solutions, or (c) no solution.

For it to have infinite number of solutions, the graph of the equations must intercept with each other at infinite points, leaving the two graphs overlaying each other.

Given the equation, 3x - 2y = 8, the other equation in a linear system to have infinite number of solutions with it must be the exact same line.

To do this, simply multiply the whole equation with a real number.

Example:

Multiplying the whole equation by 2 gives 6x - 4y = 16.

Now, 3x - 2y = 8 and 6x - 4y = 16 are equations in a linear system with infinite number of solutions.

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