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 on a graph.

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How do you solve a system of equations graphically?

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To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect. This point(s) is the solution to the system.

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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 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 is an inequality?

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An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line. Then, shade the region that satisfies the inequality.

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What does the solution set of a system of inequalities represent?

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

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What is the significance of the intersection point in a system of equations?

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The intersection point represents the solution to the system, indicating the values of the variables that satisfy all equations.