8.9A Simultaneous 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 solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the substitution method in solving linear 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 linear 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 two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

Back

The system has infinitely many solutions because the lines are the same.

Front

What is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution to the system.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.