Solving Linear Systems with Substitution Practice

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What is a linear system of equations?

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A linear system of equations is a collection of two or more linear equations involving the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

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What does it mean to solve a system of equations using substitution?

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Solving a system of equations using substitution involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of the variables.

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What is the first step in solving a system of equations by substitution?

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The first step is to isolate one variable in one of the equations, expressing it in terms of the other variable.

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How do you check if a solution is correct for a system of equations?

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To check if a solution is correct, substitute the values of the variables back into the original equations to see if they satisfy all equations.

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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 equations represent parallel lines that 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 overlap completely.

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How can you identify a system of equations with infinitely many solutions?

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You can identify a system with infinitely many solutions if, after simplifying, the equations are equivalent, such as 2x + 4y = 8 and x + 2y = 4.

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What is the substitution method used for?

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The substitution method is used to solve systems of equations by expressing one variable in terms of the other and substituting it into the second equation.

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What is the graphical interpretation of a system of linear equations?

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The graphical interpretation of a system of linear equations is that each equation represents a line on a coordinate plane, and the solution is the point(s) where the lines intersect.

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What is the significance of the y-coordinate in the solution of a system of equations?

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The y-coordinate in the solution of a system of equations represents the value of the dependent variable when the equations are satisfied.