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 if two lines are parallel in a linear system?

Back

If two lines are parallel, it means they have the same slope and will never intersect, resulting in no solution for the system.

Front

What is the solution of a linear system?

Back

The solution of a linear system is the point where the lines intersect, representing the values of the variables that satisfy all equations in the system.

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

How can you determine if a linear system has one solution, no solution, or infinitely many solutions?

Back

One solution occurs when lines intersect at a single point, no solution occurs when lines are parallel, and infinitely many solutions occur when lines coincide.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over the run between two points on the line.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you solve a system of equations 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 system of equations using elimination?

Back

To solve by elimination, add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the lines intersect at one point or coincide.