Which outcome is NOT possible for the graph of a system of two linear equations?
The lines intersect at one point so the system has one solution.
The lines intersect in two different points so the system has two solutions.
The equations graph the same line, so there are infinite solutions.
The lines do not intersect so there are no solutions.
The outcome that is NOT possible for the graph of a system of two linear equations is: The lines intersect in two different points so the system has two solutions.
Explanation: In a system of two linear equations, the lines can either intersect at a single point (one solution), be parallel (no solutions), or be the same line (infinite solutions). However, it is impossible for two lines to intersect at two different points; if they did, they would not actually be two distinct lines.
The outcome that is NOT possible is: “The lines intersect in two different points so the system has two solutions.”
This is because two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). They cannot intersect at two different points, as that would imply two different solutions for the same pair of equations, which contradicts the definition of a linear equation.
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