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 if a system of linear equations has infinitely many solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution.

Front

How can you determine if a system of linear equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

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

Back

The point where the lines intersect on a graph.

Front

What does it mean if a system of linear equations has exactly one solution?

Back

The lines intersect at a single point, which is the unique solution to the system.

Front

How do you solve a system of linear equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of linear 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 slope-intercept form of a linear equation?

Back

The form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you find the solution to a system of equations graphically?

Back

By plotting both equations on the same graph and identifying the intersection point.

Front

What is the meaning of the ordered pair (x, y) in the context of linear equations?

Back

It represents a point on the Cartesian plane, where x is the horizontal coordinate and y is the vertical coordinate.