Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is an ordered pair in the context of systems of equations?

Back

A pair of numbers (x, y) that represents a point on the coordinate plane.

Front

What is the solution of a system of equations?

Back

The point where the graphs of the equations intersect.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point into each equation; if it satisfies all equations, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The lines or curves representing each equation plotted on the same coordinate plane.

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What does it mean if two lines in a system of equations are parallel?

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The system has no solution because the lines never intersect.

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What does it mean if two lines in a system of equations coincide?

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The system has infinitely many solutions because the lines are the same.

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What is the substitution method for solving systems of equations?

Back

Solving one equation for one variable and 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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Adding or subtracting equations to eliminate one variable, making it easier to solve.