Solving Systems Using Substitution and Elimination

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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 substitution mean in solving systems of equations?

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Substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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What does elimination mean in solving systems of equations?

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Elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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When is substitution the preferred method?

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Substitution is preferred when one equation is easily solvable for one variable.

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When is elimination the preferred method?

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Elimination is preferred when the coefficients of one variable are easily manipulated to cancel out.

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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 other variable.

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How do you solve a system of equations using elimination?

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1. Align the equations. 2. Multiply one or both equations to get equal coefficients. 3. Add or subtract the equations to eliminate one variable. 4. Solve for the remaining variable.

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What is the solution to a system of equations?

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The solution is the point (x, y) where the two equations intersect, representing the values of the variables that satisfy both equations.

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

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It means 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 the equations represent the same line, and there are countless points of intersection.