Question

Determine which system below will produce infinitely many solutions.

1) −4x + 6y = 20 4x − 3y = −2
2) −2x + 4y = 18 4x − 8y = −36
3) 3x − 2y = 5 −6x − 4y = −10
4) 5x − 3y = 12 15x − 9y = 24

Answer 1

The correct answer is 2) −2x + 4y = 18 4x − 8y = −36

Explanation:

I just took the test, tried the expert verified and of course it was wrong like always

Answer 2

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=(x)/(2)+(9)/(2)} \atop {y=(x)/(2)+(9)/(2)}} \right.`

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