Flashcard - Solve Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

How do you solve a system of equations by substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection point(s) of the lines on a coordinate plane.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

Solve the system: x - 2y = 4 and 2x - y = -1.

Back

(-2, -3)

Front

Solve the system: 3x - 2y = 7 and y = 2x - 7.

Back

(7, 7)

Front

Solve the system: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either one solution (intersecting lines) or infinitely many solutions (same line).