Solve Linear Systems with Any Method

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

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What does it mean to solve a linear system?

Back

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

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What are the three methods to solve linear systems?

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

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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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How do you find the x-intercept of a linear equation?

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To find the x-intercept, set y = 0 in the equation and solve for x.

Front

How do you find the y-intercept of a linear equation?

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To find the y-intercept, set x = 0 in the equation and solve for y.

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What does it mean if a linear system has no solution?

Back

If a linear 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 linear system has infinitely many solutions?

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

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What is the substitution method?

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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 a consistent system?

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A consistent system is one that has at least one solution.