Writing and Solving Systems of Equations

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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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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 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, so every point on the line is a solution.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection points of the lines on a coordinate plane.

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What is the elimination method for 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.

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What is the purpose of writing a system of equations?

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To model real-world situations where multiple conditions must be satisfied simultaneously.

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How can you check the solution of a system of equations?

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Substitute the solution back into the original equations to see if they hold true.

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What is a linear equation?

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A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

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What are the coefficients in a system of equations?

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Coefficients are the numerical factors in front of the variables in an equation.