System 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 graphs of the equations intersect.

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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 graphs of the inequalities overlap.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a dashed or solid line. 2. Shade the region that satisfies the inequality (above or below the line).

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

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It means that 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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It means that the equations represent the same line, and every point on the line is a solution.

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How do you solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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How do you solve a system of equations using elimination?

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1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

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What is the graphical representation of the solution to a system of inequalities?

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The solution is represented by the shaded region where the graphs of the inequalities overlap.

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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, where both equations are satisfied.

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

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