Unit 4 Review - Systems of Equations

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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 on a graph.

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the lines representing the equations are parallel and never intersect.

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

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To find the solution graphically, plot both equations on the same graph and identify the point(s) where they intersect.

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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 variable.

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What is the point of intersection in a system of equations?

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The point of intersection is the solution to the system, representing the values of the variables that satisfy all equations in the system.

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How can you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they are dependent.

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What does the slope of a line represent in a system of equations?

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The slope represents the rate of change of y with respect to x. In a system, it indicates how steeply the lines rise or fall.

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How do you write a system of equations from a word problem?

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Identify the variables, translate the relationships and conditions into equations, and write them as a system.