Systems of equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

The slopes of parallel lines are the same.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the method of substitution in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the method of elimination in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

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

Back

(-3, 4)

Front

Solve the system of equations: y = 2/3x - 2 and y = -x + 3.

Back

(3, 0)

Front

Solve the system of equations: y = 4x + 1 and 3x + 2y = 13.

Back

(1, 5)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection points represent the solutions.