Solving pairs of linear equations in two variables

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What is a linear equation in two variables?

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A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

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What does the solution of a system of linear equations represent?

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The solution of a system of linear equations represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations in the system.

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How can you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and express the total or constraints as equations.

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What is the substitution method for 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 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 remaining variable.

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

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Substitute the values of the variables back into the original equations to see if they satisfy all equations.

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What is the graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) of intersection.

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What is a consistent system of equations?

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A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solutions, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.