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 graphs of the equations intersect.

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What does it mean if a system of equations has no solution?

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If a system of equations has no solution, it means that the lines represented by the equations are parallel and will never intersect.

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

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If a system of equations has infinitely many solutions, it means that the equations represent the same line, and every point on that line is a solution.

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How can you determine the solution to a system of equations graphically?

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You can determine the solution to a system of equations graphically by finding the point(s) where the graphs of the equations intersect.

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What does the slope of a line represent in a linear equation?

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The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

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What is the y-intercept in a linear equation?

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How do you solve a system of equations by graphing?

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To solve a system of equations by graphing, plot each equation on the same graph and identify the point(s) where they intersect.

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The solution is (-1, -2).

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The solution is the point where the two lines intersect, which can be found by graphing or solving algebraically.