Solving 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 simultaneously.

Front

What is the graphical representation of a system of linear equations?

Back

The intersection point(s) of the lines representing the equations on a graph.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted 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 representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

Solve the system: 2x + 9y = -7 and 6x - 3y = 9.

Back

(1, -1)

Front

Solve the system: x + 2y = -3 and x - y = -12.

Back

(-9, 3)

Front

Solve the system: x + 6y = 17 and x - 3y = 8.

Back

(11, 1)