System of Equations

Front

What is a system of equations?

Back

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

Front

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 the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

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What is a solution to a system of equations?

Back

A set of values for the variables that makes all equations true.

Front

What is an example of a system of equations?

Back

y = 2x + 1 and y = 4x - 1.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

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, it's a solution.

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What is substitution method in solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is elimination method in solving systems of equations?

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Adding or subtracting equations to eliminate one variable, making it easier to solve.