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 if a system of equations has one solution?

Back

The lines intersect at exactly one point, representing a unique solution for the variables.

Front

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

Back

The lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

Front

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

Back

The lines coincide, meaning they are the same line and have an infinite number of points in common.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

What is the graphical method for solving systems of equations?

Back

A method where you graph the equations on a coordinate plane and find the point(s) of intersection.

Front

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

Back

(3, 0)

Front

What is the solution to the system: 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)