Systems 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 if a system of equations has infinite solutions?

Back

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

Front

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

Back

The equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has exactly one solution?

Back

The equations represent intersecting lines, which cross at one point.

Front

What is the substitution method 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

Solve the system of equations: 2y + x = -15, x = 3y.

Back

(-9, -3)

Front

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

Back

(1, 5)

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the first step in solving a system of equations using substitution?

Back

Solve one of the equations for one variable.

Front

What does the term 'consistent' mean in relation to systems of equations?

Back

A system is consistent if it has at least one solution.