Unit 4 Review - Systems of Equations

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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 if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

Back

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

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How do you determine the number of solutions in a system of equations?

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By analyzing the slopes and y-intercepts of the lines: if slopes are equal and y-intercepts are different, no solution; if slopes are equal and y-intercepts are the same, infinitely many solutions; if slopes are different, one solution.

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What is the graphical representation of a system of inequalities?

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The solution set is represented by the shaded region where the inequalities overlap on a graph.

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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 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.

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What does it mean for two lines to be perpendicular in the context of systems of equations?

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Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.

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

Back

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How can you tell if a point is a solution to a system of equations?

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A point is a solution if it satisfies all equations in the system when substituted into them.