Systems of Equations

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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 to solve a system of equations by elimination?

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

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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 graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

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What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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How do you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which means they never intersect.

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How do you determine 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 overlap completely.

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What is the first step in solving a system of equations using substitution?

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The first step is to isolate one variable in one of the equations.

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If y = 2x + 3, what is y when x = 4?

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y = 2(4) + 3 = 8 + 3 = 11.

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What is the elimination method used for?

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The elimination method is used to eliminate one variable by adding or subtracting equations, simplifying the system to one equation with one variable.