Honors Algebra - Unit 5 Review - Systems of Equations 2024

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What is a system of equations?

Back

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?

Back

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 infinite solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

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How do you determine the solution of 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 represent a system of equations in matrix form?

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A system of equations can be represented in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

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What is a point that satisfies a system of inequalities?

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A point that satisfies a system of inequalities is a point that lies in the region defined by all the inequalities.