Carnegie Systems Review

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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 represent a system of equations graphically?

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A system of equations can be represented graphically by plotting each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

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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 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 remaining variable.

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap on a graph.

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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, use a dashed line for < or > and a solid line for ≤ or ≥. Shade the appropriate region based on the inequality.

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What is the meaning of the solution (3, -3) in a system of equations?

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The solution (3, -3) means that when x = 3 and y = -3, both equations in the system are satisfied.

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What does it mean if a system of equations has no solution?

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A system of equations has no solution if the lines representing the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.