TEKS A.2I: Writing 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 on a graph.

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How do you solve a system of equations graphically?

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To solve a system of equations graphically, plot each equation on the same graph and identify the point(s) where the lines intersect. This point(s) represents the solution.

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What does it mean for a system of equations to be consistent?

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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 does it mean for a system of equations to be inconsistent?

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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 the substitution method for 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 for 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 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 is non-negative.

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How can you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and then write them as a system of equations.

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

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Coefficients represent the rate of change or the slope of the line in the context of the variables they are associated with.

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What is the role of the constant term in a linear equation?

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The constant term represents the y-intercept of the line, indicating where the line crosses the y-axis.