Solving Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean to solve a linear system?

Back

To solve a linear system means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line on a coordinate plane.

Front

What is the point of intersection in a linear system?

Back

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

Front

What are the possible outcomes when solving a linear system?

Back

1. One solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinitely many solutions (the lines coincide).

Front

How do you solve a linear system using substitution?

Back

To solve by substitution, solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a linear system using elimination?

Back

To solve by elimination, add or subtract the 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 slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you determine if a point is a solution to a linear system?

Back

Substitute the point's coordinates into each equation. If both equations are true, the point is a solution.