Q2,W6,A1 System of Equations (mid)

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 when a system of equations has one solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

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

Back

It means the graphs of the equations are parallel and never intersect.

Front

What does it mean when a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

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

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate grid.

Front

What is an ordered pair in the context of a system of equations?

Back

An ordered pair (x, y) represents a solution to the system if it satisfies all equations.

Front

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

Back

(−2, −1) is the solution.

Front

Solve the system of equations: 2x + 3y = 6 and x - y = 1.

Back

(3, 0) is the solution.