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One Solution for a System of Linear Equations

Explanation

One Solution for a System of Linear Equations

The graph of a system that has one solution might look similar to the graph shown. Specifically, it will show that the lines intersect exactly once. The point of intersection is the solution to the system.

One solution linear system of equations.svg

In contrast to parallel lines, lines that intersect once must have unequal slopes. For example, the system shown must have exactly one solutin as the two lines have different slopes. {y=-1x+5y=3x2\begin{cases}y=\text{-} 1x+5 \\ y=3x-2 \end{cases}