Identify the type of system of equations and select the most correct meaning below.2𝑥−5𝑦=66𝑥−15𝑦=30 Group of answer choicesAn independent system; the lines will cross in only one place so there is only one solution.An inconsistent system; there is really only one line so any of the infinite number of points on that line is a solution.An inconsistent system; the parallel lines will never cross so there is no solution.A dependent system; there is really only one line so any of the infinite number of points on that line is a solution.A dependent system; the parallel lines will never cross so there is no solution.
Question
Identify the type of system of equations and select the most correct meaning below.2𝑥−5𝑦=66𝑥−15𝑦=30 Group of answer choicesAn independent system; the lines will cross in only one place so there is only one solution.An inconsistent system; there is really only one line so any of the infinite number of points on that line is a solution.An inconsistent system; the parallel lines will never cross so there is no solution.A dependent system; there is really only one line so any of the infinite number of points on that line is a solution.A dependent system; the parallel lines will never cross so there is no solution.
Solution
The given system of equations is:
2x - 5y = 6 6x - 15y = 30
First, let's simplify the second equation by dividing every term by 3:
2x - 5y = 10
Now, we can see that the two equations are not the same. The first equation is 2x - 5y = 6 and the simplified second equation is 2x - 5y = 10. The left sides of the equations are the same, but the right sides are different. This means that the lines represented by these equations are parallel and will never intersect.
Therefore, the correct answer is: An inconsistent system; the parallel lines will never cross so there is no solution.
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