Flashcard 5.2-5.4 Math 1

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

Front

What does it mean for two lines to intersect?

Back

When two lines intersect, it means they cross at a single point, which represents the unique solution to the system of equations.

Front

What is the solution to a system of linear equations?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

If a system of equations has no solution, it means the lines are parallel and will never intersect.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning they have the same slope and y-intercept.

Front

What is the value of y in the equation y = -2x - 4 when x = 2?

Back

When x = 2, y = -2(2) - 4 = -4 - 4 = -8.

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure the equations represent the total or constraints given.

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 does the term 'slope' refer to in a linear equation?

Back

The slope refers to the steepness of the line, calculated as the rise over run (change in y over change in x).