System of Equations Word Problems

Front

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 to solve a system of equations by graphing?

Back

To solve a system of equations by graphing means to plot each equation on a graph and identify the point(s) where they intersect, which represents the solution.

Front

What is the meaning of 'no solution' in a system of equations?

Back

'No solution' means that the equations represent parallel lines that never intersect, indicating there are no values that satisfy both equations.

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What does 'infinitely many solutions' mean in a system of equations?

Back

'Infinitely many solutions' means that the equations represent the same line, so every point on the line is a solution.

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How do you represent a system of equations algebraically?

Back

A system of equations can be represented as two or more equations, such as: x + y = 10 and x - y = 2.

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What is the substitution method for 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 for 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 is a consistent system of equations?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that do not intersect.

Front

What is a dependent system of equations?

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