Solve Systems of Linear Equations by Substitution and Elmination

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

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

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Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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What does it mean to solve a system of equations by elimination?

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Solving by elimination 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 first step in solving a system of equations by elimination?

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The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

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How do you determine if a system of equations has infinite solutions?

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A system has infinite solutions if the equations represent the same line, meaning they are dependent and have the same slope and y-intercept.

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

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The graphical representation is the intersection points of the lines represented by the equations. Each line corresponds to one equation.

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What is the significance of the x-value in the solution of a system of equations?

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The x-value represents the horizontal coordinate of the intersection point of the two lines, indicating the value of the variable x that satisfies both equations.

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

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The y-value represents the vertical coordinate of the intersection point of the two lines, indicating the value of the variable y that satisfies both equations.

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

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A system has no solution if the lines represented by the equations are parallel, meaning they never intersect.

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How can you check your solution to a system of equations?

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You can check your solution by substituting the values of the variables back into the original equations to see if they hold true.