Systems of Equations & Inequalities 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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What does it mean to solve a system of equations by graphing?

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To solve a system of equations by graphing means to plot each equation on the same coordinate plane and identify the point(s) where they intersect.

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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 variable.

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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 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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What does it mean to graph an inequality?

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Graphing an inequality involves shading the region of the graph that satisfies the inequality, using a solid line for 'greater than or equal to' and 'less than or equal to', and a dotted line for 'greater than' and 'less than'.

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What is the difference between a solid line and a dotted line when graphing inequalities?

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A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dotted line indicates that points on the line are not included (> or <).

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How do you write a system of inequalities from a word problem?

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Identify the constraints and objectives in the problem, then express them as inequalities using variables to represent the quantities involved.

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What is the feasible region in a system of inequalities?

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The feasible region is the area on the graph that satisfies all the inequalities in the system, representing all possible solutions.

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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.