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.

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What does it mean to graph a system of linear equations?

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It involves plotting the equations on a coordinate plane to find their intersection point(s), which represent the solution(s).

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

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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 substituting that expression into the other equation.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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

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If two lines are parallel, it means they have the same slope and will never intersect, indicating that there is no solution to the system.

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

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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What is a unique solution in a system of linear equations?

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A unique solution occurs when the two lines intersect at exactly one point, representing a single solution for the system.

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

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By analyzing the slopes and y-intercepts of the lines: if slopes are different, one solution; if slopes are the same and intercepts are different, no solution; if slopes and intercepts are the same, infinitely many solutions.

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What is the first step in using the substitution method?

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The first step is to solve one of the equations for one variable in terms of the other variable.