Systems of Equations - Review

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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 to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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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 variable.

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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 does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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How can you check if your solution to a system of equations is correct?

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You can check your solution by substituting the values back into the original equations to see if they hold true.

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What is the importance of the coefficients in a system of equations?

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The coefficients determine the slope and position of the lines represented by the equations, affecting the number of solutions.

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.