A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.

Let's look at the four equations, with each solved as needed, into y = mx + b form.

A: 2x + y = 5

y = 5 - 2x

y = -2x + 5

Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.

B: y = 2x + 5

Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.

C: 2x - 4y = 10

-4y = 10 - 2x

-4y = -2x + 10

y = 2/4x -10/4

Here the slopes are different, so, like A this is not a good choice.

D: 2y - 4x = -10

2y = =10 + 4x

2y = 4x - 10

y = 2x - 5

Compared to y = 2x + 5 we have the same slopes and different y intercepts. The lines will be parallel and the system is inconsistent.

Thus, D is the best choice.

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3 years ago

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What do you think about when you hear the phrase "system of equations"? In other words, what do you already know about systems o

Reptile [31]

Basically the question is asking YOU when you hear “system of equations” what do you think about it - what do you already know about system of equations. Basically. Btw enjoy this picture.