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 word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does it mean for two equations to be consistent?

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Two equations are consistent if they have at least one solution in common.

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What does it mean for two equations to be independent?

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Two equations are independent if they represent different lines that intersect at exactly one point.

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What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

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How can you determine the number of solutions in a system of equations?

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By analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they are parallel, there are no solutions; if they are the same line, there are infinitely many solutions.

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

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Substitute the values of the variables back into the original equations to verify that both equations are satisfied.

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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 the lines intersect.