Question

A system of linear equations can have zero, one, or an infinite number of solutions.

Describe a rule that can be used to determine the number of solutions a system of linear
equations will have.

Answer 1

If the linear equations form parallel lines or if the answer is not true like 0=8 or 5=18 it means the linear equations have no solutions. If the linear equations form 2 lines that are on top of each other or the answer is true for example 0=0 or 5=5 then the linear equations will have infinitely many solutions. If a linear equation gives you a single answer like x= 7 an y=9 then the linear equation only has one solution

Answer 2

A system of linear equations is a set of two or more linear equations in the same variables.

y=x+1 Equation 1
y=2x-7 Equation 2