Algebra midterm review part1

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 system of equations to have one solution?

Back

It means that the graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solutions?

Back

It means that the graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that the equations represent the same line, so they intersect at every point on that line.

Front

How do you simplify the equation 3x - 8 = 3(x - 4) + 1?

Back

Combine like terms to find that it simplifies to 3x - 8 = 3x - 12 + 1, which leads to no solutions.

Front

What is the product of (x - 6)²?

Back

The product is x² - 12x + 36.

Front

What is the domain of a function?

Back

The set of all possible input values (x-values) for which the function is defined.

Front

How do you find the domain of the graph y = 2x + 1?

Back

The domain is all real numbers, as there are no restrictions on x.

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 slope of a line represent?

Back

The slope represents the rate of change of y with respect to x.