Systems: Substitution

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 has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an equivalent expression.

Front

Solve for x and y: 2x + 3y = 12 and x - y = 1.

Back

(3, 2)

Front

Solve for x and y: x + 2y = 10 and 3x + y = 5.

Back

No Solution

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines on a coordinate plane.

Front

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

Back

Isolate one variable in one of the equations.