Solving Systems

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 if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

They have infinitely many solutions because they overlap completely.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

There is exactly one solution to the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) of intersection.

Front

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

Back

(3, 0)

Front

What is the solution to the system of equations 3x - 2y = 4 and 6x + 4y = 8?

Back

No solution (the lines are parallel).

Front

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

Back

(3, 2)