Systems of Equations and Inequalities

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What is a system of equations?

Back

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 solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinite solutions (the lines are the same).

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How do you graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and plot them on a coordinate plane, then connect the points with a straight line.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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

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How do you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

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What is the substitution method for 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 for 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 does it mean for a system of equations to have infinite solutions?

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A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you write an inequality from a word problem?

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Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using inequality symbols (>, <, ≥, ≤).