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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How do you solve a system of linear equations graphically?

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To solve a system of linear equations graphically, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect.

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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 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 other 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 shade the region that satisfies the inequality.

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What does it mean for a point to be a solution to a system of equations?

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A point is a solution to a system of equations if it satisfies all equations in the system, meaning it makes all equations true when substituted.

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

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The symbol '>' indicates that one value is greater than another, while '≥' indicates that one value is greater than or equal to another.

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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 simultaneously.