Archive - Systems of Linear Equations

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What is a system of linear equations?

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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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How do you solve a system of linear equations using substitution?

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

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The lines representing the equations on a graph. The point of intersection represents the solution.

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What does it mean if two lines are parallel in a system of linear equations?

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The system has no solution because the lines never intersect.

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What does it mean if two lines coincide in a system of linear equations?

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The system has infinitely many solutions because the lines are the same.

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What is the elimination method for solving systems of linear equations?

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A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is the x-intercept of a linear equation?

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The point where the line crosses the x-axis, found by setting y=0 and solving for x.

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What is the y-intercept of a linear equation?

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The point where the line crosses the y-axis, found by setting x=0 and solving for y.

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How do 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 a word problem involving systems of linear equations?

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A real-world scenario that can be modeled with two or more linear equations to find unknown values.