TEKS A.2I: Writing Systems of Equations

Front

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 set of values that satisfy all equations in the system.

Front

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

Back

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 the variable 'x' typically represent in a system of equations?

Back

In a system of equations, 'x' usually represents one of the unknown quantities that need to be solved for.

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What does the variable 'y' typically represent in a system of equations?

Back

In a system of equations, 'y' usually represents another unknown quantity that is related to 'x'.

Front

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

Back

Coefficients indicate the relationship between the variables. They show how much one variable changes in relation to another.

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

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

Front

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

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines or curves on a coordinate plane, where the intersection points represent the solutions.

Front

How can you solve a system of equations graphically?

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To solve graphically, plot each equation on the same graph and identify the intersection points, which represent the solutions.

Front

What is substitution in the context of solving systems of equations?

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Substitution is a method where you solve one equation for one variable and substitute that expression into the other equation.