8.EE.8 Systems of Equations

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean if a system of equations has one solution?

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It means that the lines represented by the equations intersect at exactly one point.

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

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It means that 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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It means that the lines represented by the equations coincide, or are the same line, resulting in an infinite number of intersection points.

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How do you find the solution to a system of equations graphically?

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You graph both equations on the same coordinate plane and identify the point(s) where they intersect.

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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 then 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 is the significance of the coefficients in a system of equations?

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Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

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How can you tell if two equations represent parallel lines?

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Two equations represent parallel lines if they have the same slope but different y-intercepts.

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What is the general form of a linear equation?

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