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 it mean to solve a system of linear equations?

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To solve a system of linear equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What are the three main methods for solving systems of linear equations?

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The three main methods are: 1) Graphing, 2) Substitution, 3) Elimination.

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How do you solve a system of equations by substitution?

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To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

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What is the elimination method?

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

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If a system has no solution, 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 infinite solutions?

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If a system has infinite solutions, it means the equations represent the same line, and there are countless points of intersection.

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

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You can check by substituting the solution back into the original equations to see if both equations are satisfied.

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What is the graphical representation of a linear equation?

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The graphical representation of a linear equation is a straight line on a coordinate plane.

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What is the point of intersection in a system of equations?

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The point of intersection is the point where the graphs of the equations meet, representing the solution to the system.