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 to the system is the set of values that satisfy all equations simultaneously.

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.

Front

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 we are trying to solve for.

Front

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 we are trying to solve for, often related to 'x'.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations and manipulate them (by addition or subtraction) to eliminate one variable.

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What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no values for the variables that satisfy all equations.

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What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution to the system.

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How can you check if your solution to a system of equations is correct?

Back

Substitute the values of the variables back into the original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate plane, where the intersection point(s) represent the solution(s).