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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

What is an ordered pair in the context of systems of equations?

Back

A pair of numbers (x, y) that represents a point on the coordinate plane.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you solve a system of equations by 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 by elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the y-coordinate of the solution to the system: x - 2y = 1 and x + 4y = 7?

Back

1

Front

Solve the system: 3x + 2y = 16 and 7x + y = 19. What is the solution?

Back

(2, 5)