Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean to solve a system of linear equations?

Back

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

Front

What is substitution in the context of solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

What is the elimination method for solving systems of equations?

Back

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

Front

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

Back

The lines represented by 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, meaning every point on the line is a solution.

Front

How can you determine the solution of a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

What is the solution to the system: 3x + 4y = 10 and 6x + 8y = 20?

Back

Infinitely Many Solutions

Front

What is the solution to the system: x + y = 5 and x - y = 1?

Back

(3, 2)