Systems of Equations and Inequalities

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean for a system of equations to have no solution?

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A system has no solution when the equations represent parallel lines that never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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A system has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

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How do you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation. If both equations are true, the point is a solution.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection of the lines represented by the equations on a coordinate plane.

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method for solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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(1, 2)

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Infinitely many solutions

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Yes