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 for two lines to be parallel?

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Two lines are parallel if they have the same slope and will never intersect.

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

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How do you solve a system of equations using elimination?

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To solve by elimination, you manipulate the equations to eliminate one variable, allowing you to solve for the other variable.

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The y-intercept is the point where the line crosses the y-axis, which is (0, 2) in this case.

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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 represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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

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You can determine the number of solutions by comparing the slopes and y-intercepts of the equations.

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What is the standard form of a linear equation?

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