Solving Systems of Equations

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

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What does it mean for a system of equations to have infinite solutions?

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It means that the equations represent the same line, so every point on the line is a solution.

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How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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How do you solve a system of equations by elimination?

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1. Align the equations. 2. Multiply one or both equations to get opposite coefficients. 3. Add or subtract the equations to eliminate one variable.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection points of the lines representing each equation.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How can you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into both equations. If both equations are true, the point is a solution.

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What is the meaning of the coefficients in a linear equation?

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Coefficients represent the rate of change of the dependent variable with respect to the independent variable.

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What is the purpose of graphing a system of equations?

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Graphing helps visualize the solutions and understand the relationship between the equations.