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identify the type of system of equations for the system below

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2 Answers

1. If system of equations has exactly one solution, the system is consistent independent.
2. If there are infinitely many solutions, the system is consistent dependent.
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2y = 4 - 6x  is an equation, but "3y + 9x + 6" is an expression.

So, if
I.   2y = 4 - 6x
     3y = 9x + 6
the system is consistent independent.
II.  2y = 4 - 6x
     3y + 9x = 6
the system is consistent dependent.

Maria, this is mathematics and you have to copy the problem exactly as it appear in the original source.

I'm going to assume you are asking whether there is one solution, no solution, or infinite solutions (meaning they are the same line). I am also going to assume that you meant to type 3y = 9x + 6, not 3y + 9x + 6.

Equation A:     2y = 4 - 6x

Equation B:     3y = 9x + 6

I would start out by putting both equations in y = mx + b form. This will help us determine if they are parallel or perpendicular or the same line. For equation A I'm going to divide everything by 2.

A:     2y = 4 - 6x     ->     y = 2 - 3x     ->     y = -3x + 2

And for equation B I'm going to divide everything by 3.

B:     3y = 9x + 6     ->     y = 3x + 2

We can tell that they have the same y-intercept of 2, which means that they at least intersect once. They do not have the same slope, however, so they are not the same line. Therefore this system has only one solution.

Comments

Since there is at least one solution, then the system is consistent.

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