14.5 Q Solving Systems of Equations-Review

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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 set of values that satisfy all equations simultaneously.

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What does it mean to eliminate a variable in a system of equations?

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Eliminating a variable means to manipulate the equations in such a way that one variable is removed, allowing for easier solving of the remaining 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 possible to solve for the other variable.

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How do you identify which variable to eliminate?

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Choose the variable that can be easily eliminated by aligning coefficients in the equations, often by multiplying one or both equations.

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What is the solution to a system of equations?

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The solution is the point (or points) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

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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, indicating that there are no values for the variables that satisfy both equations.

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

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Substitute the values of the variables back into the original equations to see if they hold true.

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Solve for x and y: 2x + 3y = 12 and x - y = 1.

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(3, 2) is the solution.

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