5.1 flashcard Alg 1

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the graphs of the equations intersect.

Front

How do you estimate the solution of a system of linear equations using a graph?

Back

To estimate the solution, plot the graphs of the equations on the same coordinate plane and identify the point where they intersect.

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the significance of the point of intersection in a system of linear equations?

Back

The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations in the system.

Front

What is the standard form of a linear equation?

Back

Front

How do you convert a linear equation from slope-intercept form to standard form?

Back

Front

What is the slope-intercept form of a linear equation?

Back

Front

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

Back

A system of equations is inconsistent if there is no solution, meaning the lines represented by the equations are parallel and never intersect.