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 equations by elimination?

Back

It 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

What is the graphical representation of intersecting lines?

Back

The lines cross at a single point, indicating one unique 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

What is the solution to the system: 7x - 9y = 29 and 7x + 2y = -15?

Back

(-1, -4)

Front

What is the solution to the system: 3x + 7y = 23 and -3x - 7y = -17?

Back

No solution.

Front

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

Back

(1, 0)

Front

What does it mean if two lines are skew?

Back

They do not intersect and are not parallel, existing in different planes.