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In the system of equations -5x - y + 5 = 0 and 5x + y = 5, what type of solution does it have?

User Pandawan
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Final answer:

Adding the given system of equations results in a false statement, indicating the system has no solution, which means graphically, it represents parallel lines that never intersect.

Step-by-step explanation:

The system of equations given are -5x - y + 5 = 0 and 5x + y = 5. To determine what type of solution this system has, we can add both equations. Since the x terms and y terms are additive inverses of each other, they will cancel out when we add the equations together, resulting in a true statement 0 = 5.

This outcome signifies that our original system of equations has no solution, making it an inconsistent system. In a graphical representation, this means that the two equations would represent two parallel lines which never intersect.

In such systems, the coefficients of the x and y variables will always be multiples of each other and the constants on the right side of the equations will not be multiples, leading to parallel, non-intersecting lines.

User Methmal Godage
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