What do you do when the variable disappears, while solving a system of equations, by adding them together using the elimination method: 30x  15y = 30 30x + 15y = 30  0 = 0 = infinite solutions When the variable disappears and you get a true statement, such as 0 = 0, then there are "infinite solutions". This means, the two lines intersect in an infinite number of points. In other words, the two equations are equivalent, and would create the same line when graphed. When the variable disappears and you get a false statement, such as 0 = 3, then there is "no solution". This means, the two lines would not intersect. In other words, the two equations, when graphed, would create parallel lines. © Algebra House
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