Solving Systems of Linear Equations

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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 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 substitution method in 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 graphical interpretation of a system of linear equations?

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The graphical interpretation involves plotting the equations on a graph; the solution is the point(s) where the lines intersect.

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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 are parallel, meaning they never intersect.

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What does it mean 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 every point on the line is a solution.

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How do you determine the number of solutions in a system of equations?

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You can determine the number of solutions by analyzing the slopes and intercepts of the lines represented by the equations.

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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 solve one of the equations for one variable in terms of the other variable.

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What is the elimination method's first step?

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The first step is to align the equations and manipulate them (by multiplying if necessary) to eliminate one variable.

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Solve the system of equations by elimination: -x + y = -13 and -8x - 4y = -8.

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(5, -8)