Solving Systems of Equations

Front

Define 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 simultaneously.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you solve a system of linear equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

How do you solve a system of linear equations using elimination?

Back

1. Align the equations. 2. Multiply one or both equations to obtain opposite coefficients for one variable. 3. Add or subtract the equations to eliminate one variable.

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means that the equations represent the same line, and there are countless points of intersection.

Front

Solve the system: 3x - 4y = 14 and 5x + y = 8.

Back

(2, -2)

Front

Solve the system: y = x + 3 and -2x + 2y = 6.

Back

infinite solutions

Front

Solve the system: y = -4x + 5 and 2x - 3y = 13.

Back

(2, -3)