Systems of Equations Practice 1

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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 point(s) where the equations intersect.

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What does it mean if a system of equations has no solution?

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It means that the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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

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How do you solve a system of equations using the substitution method?

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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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How do you solve a system of equations using the elimination method?

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1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) to the system.

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

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It means they represent the same line, resulting in infinitely many solutions.

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What is the substitution method?

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A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.