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:
`(a_1)/(a_2)\\eq (b_1)/(b_2)`;
2. no solutions, when:
`(a_1)/(a_2) = (b_1)/(b_2) \\eq (c_1)/(c_2)`;
3. infinitely many solutions, when:
`(a_1)/(a_2) = (b_1)/(b_2) = (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.