Question

a system of two linear equations has infinitely many solutions. one of the equations in the system is y-3x=-3.write an equation that can be used to complete the system so that it has infinitely many solutions.solve your system using any method to show that it has infinitely many solutions.

Answer 1

the other equation could be

2y - 6x = -6

Solving:-

y - 3x = -3..........(1)
2y - 6x = -6........(2)
multiplyng the first equation by 2 gives
2y - 6x = -6

so equations (1) and (2) are the same equation
If we graph them they will be the same line
Every point on that line will be a solution.

So there are infinitely many solutions