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 to solve a system of equations graphically?

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To solve a system of equations graphically means to plot the equations on a graph and find the point(s) where they intersect, which represents the solution.

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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 remaining variable.

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What is a consistent system of equations?

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A consistent system of equations has at least one solution, meaning the lines intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solutions, meaning the lines are parallel and never intersect.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

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How do you represent a real-world problem as a system of equations?

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Identify the variables, write equations based on the relationships described in the problem, and ensure they reflect the constraints given.

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

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Coefficients represent the rate of change or the relationship between variables in the equations, affecting the slope and position of the lines.

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How can you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.