#1. Algebra 2 - Systems of Equations 1

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

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A system has no solution if the equations represent parallel lines that 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 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 represent a system of equations graphically?

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A system of equations can be represented graphically by plotting each equation on the same coordinate plane and identifying the intersection points.

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What is the first step in solving a system of equations using substitution?

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The first step is to solve one of the equations for one variable in terms of the other variable.

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What is the first step in solving a system of equations using elimination?

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The first step is to align the equations and manipulate them (if necessary) to eliminate one variable when added or subtracted.

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How can you check if your solution to a system of equations is correct?

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You can check your solution by substituting the values back into the original equations to see if they hold true.