System 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 the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

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

Back

The system has no solution because the lines never intersect.

Front

What is an example of a system of equations with one solution?

Back

y = 2x + 1 and y = -x + 4 intersect at (1, 3).

Front

What is an example of a system of equations with no solution?

Back

y = 2x + 1 and y = 2x - 3 are parallel lines.

Front

What is an example of a system of equations with infinitely many solutions?

Back

y = 2x + 1 and 2y = 4x + 2 are the same line.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point(s) where the lines intersect.

Front

What is the substitution method in solving systems of equations?

Back

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

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What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate a variable.