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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 in the system.

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How do you solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.

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What is the graphical interpretation of a system of equations?

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The solutions to a system of equations can be represented as the points where the graphs of the equations intersect.

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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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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 variable.

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What is a consistent system of equations?

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A consistent system has at least one solution, which can be either a unique solution or infinitely many solutions.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines.

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How can you represent a system of equations in matrix form?

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A system of equations can be represented in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

Front

What is the substitution method?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.