TEKS A.2I: Writing 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 to the system is the set of values that satisfy all equations simultaneously.

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How do you represent a system of equations graphically?

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A system of equations can be represented graphically by plotting each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

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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. It can be either independent (one solution) or dependent (infinitely many solutions).

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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. This occurs when the equations represent parallel lines that 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 to find the values of both variables.

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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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How do you write a system of equations from a word problem?

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To write a system of equations from a word problem, identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same scenario.

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

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Coefficients represent the relationship between variables in an equation. They determine the slope of the line when graphed and affect the solution of the system.

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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. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the meaning of the slope in a linear equation?

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The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.