Question

Create a system of linear equations with infinitely many solutions. In your final answer, include the system of equations and the graphs of the lines.

Answer 1

A system of linear equations $\left \{ {{a_1x+b_1y=c_1} \atop {a_2x+b_2y=c_2}} \right.$ has:
1. unique solution, when: $\frac{a_1}{a_2}\neq \frac{b_1}{b_2}$;
2. no solutions, when: $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$;
3. infinitely many solutions, when:  $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.
According to the part 3 you can create such system:
$\left \{ {{x-2y=3} \atop {_2x-4y=6}} \right.$
Graphs (the same line) are shown on the added picture.