Algebra - Unit 5 Review - 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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How do you determine if a point is a solution to a system of equations?

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Substitute the coordinates of the point into each equation. If the point satisfies all equations, it 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 point(s) of the lines represented by the equations.

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What does it mean for a system of equations to be consistent?

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A consistent system has at least one solution, meaning the lines intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system has no solutions, meaning the lines are parallel and never 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 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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How can you represent a system of inequalities graphically?

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Graph each inequality on the same coordinate plane, shading the region that satisfies each inequality.

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What is the significance of the solution to a system of inequalities?

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The solution represents all the points that satisfy all inequalities in the system, often forming a shaded region on a graph.

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What is a linear equation?

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