P3. Flashcard #2: 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 set of values that satisfy all equations simultaneously.

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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 make all equations in the system true.

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What are the three possible outcomes when solving a system of equations?

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1. One solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinitely many solutions (the lines coincide).

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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 remaining variable.

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How do you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection of the lines corresponding to the equations. The point of intersection represents the solution.

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What does it mean if two equations in a system are identical?

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If two equations are identical, they represent the same line, resulting in infinitely many solutions.

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

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What is the first step in using the substitution method?

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