Question

Determine which system below will produce infinitely many solutions.

Answer 1

The right answer is 2)

$\left \{ {{-2x+4y=18} \atop {4x-8y=-36}} \right.$

Recall that, in systems of linear equations, when the number of equations is the same as the number of variables there is likely to be a solution. This is not guaranteed, but for sure it is possible to find a solution.

So the case of Infinitely many solutions claims for the same lines. These systems are called consistent. Thus, if we isolate the variable $y$ of each equation we have:

$\left \{ {{y=\frac{x}{2}+\frac{9}{2}} \atop {y=\frac{x}{2}+\frac{9}{2}}} \right.$

As you can see these equations are the same, therefore they represent the same line as indicated in the Figure below.