Systems of Equations and Inequalities

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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?

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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 graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection point(s) of the lines representing each equation on a coordinate plane.

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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 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 every point on the line is a solution.

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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 is the difference between '>' and '≥' in inequalities?

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'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How do you find the solution to a system of equations algebraically?

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You can find the solution algebraically using methods such as substitution, elimination, or graphing.