Systems of equations

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What is a system of equations?

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A set of two or more equations with the same variables.

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What does it mean for a system of equations to have a unique solution?

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It means there is exactly one set of values for the variables that satisfies all equations in the system.

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What does it mean for a system of equations to have no solution?

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It means that the equations represent parallel lines that never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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It means that the equations represent the same line, so any point on the line is a solution.

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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.

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What is the substitution method?

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A method for solving systems of equations by replacing one variable with an expression derived from another equation.

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What is the elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

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How can you determine if two equations are independent?

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If their graphs intersect at exactly one point, they are independent.

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What is the graphical representation of a system of equations?

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The graphs of the equations plotted on the same coordinate plane.

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What is the y-coordinate of the solution to the system of equations x - 2y = 1 and x + 4y = 7?

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