Systems of Equations

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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 to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What are the possible outcomes when solving a system of equations?

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1. One unique solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinitely many solutions (the lines coincide).

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How can you graphically represent a system of equations?

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By plotting each equation on the same coordinate plane and identifying the point(s) where they intersect.

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What is the substitution method in solving systems of equations?

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

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What is the elimination method in 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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What does it mean for two lines to be parallel in the context of systems of equations?

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Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect and thus have no solution.

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What does it mean for two lines to be coincident?

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Two lines are coincident if they lie on top of each other, meaning they have infinitely many solutions as every point on the line is a solution.

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How can you check if your solution to a system of equations is correct?

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You can check by substituting the solution back into the original equations to see if both equations are satisfied.

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What is the graphical interpretation of a unique solution in a system of equations?

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A unique solution is represented by the point where the two lines intersect on a graph.