Systems of Equations with Elimination and Substitution

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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 is the elimination method?

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The elimination method is a technique for solving systems of equations by adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is the substitution method?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of the variables.

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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 obtain opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable. 4. Solve for the remaining variable.

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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. 4. Substitute back to find the other variable.

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

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A system of equations has no solution if the lines represented by the equations are parallel, meaning they 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 of equations 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 first step in using the elimination method?

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The first step is to align the equations and, if necessary, multiply one or both equations to make the coefficients of one variable opposites.

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What is the first step in using the substitution method?

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The first step is to solve one of the equations for one variable in terms of the other variable.

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Example of elimination method: Solve the system: 2x + 3y = 6 and 4x - 3y = 12.

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Solution: (3, 0).