Dec 13 HW - Chapter 5 Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does the slope of a line represent?

Back

The rate of change of y with respect to x; it indicates the steepness and direction of the line.

Front

What is the y-intercept of a line?

Back

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

Front

How can you determine if a point lies on a line given by an equation?

Back

Substitute the x-value of the point into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What does it mean for a system of equations to be dependent?

Back

The system has infinitely many solutions, meaning the equations represent the same line.

Front

How do you find the intersection point of two lines graphically?

Back

Plot both lines on the same graph and identify the point where they cross.