Flashcard 2.1

Front

What is the solution to the equation -3x + 7y = 5x + 2y when x = -5?

Back

-8

Front

Define a linear equation.

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one, and it can be written in the form ax + by = c.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set.

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

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

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 lies on a line represented by a linear equation?

Back

Substitute the x and y coordinates of the point into the equation; if the equation holds true, the point lies on the line.

Front

What is the process to solve a system of linear equations?

Back

You can solve a system of linear equations using substitution, elimination, or graphing methods.

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 that satisfies all equations simultaneously.