13.4 Picking the Best Method to Solve Systems of Equations

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What is the Elimination Method in 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 the Substitution Method in solving systems of equations?

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

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What is the Graphing Method in solving systems of equations?

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The Graphing Method involves graphing both equations on the same coordinate plane and identifying the point(s) where they intersect.

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When is it best to use the Elimination Method?

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The Elimination Method is best used when the coefficients of one variable are the same or can be easily manipulated to be the same.

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When is it best to use the Substitution Method?

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The Substitution Method is best used when one equation is easily solvable for one variable.

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

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A system of equations has no solutions if the lines representing 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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A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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How do you determine the best method to solve a system of equations?

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Consider the structure of the equations, the coefficients, and whether you can easily isolate a variable or graph the equations.

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What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

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The solution is (3, 0).

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What is the solution to the system of equations: x + y = 8 and 2x - y = 3?

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The solution is (5, 3).