ALGEBRA II ACP REVIEW

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. Solutions are the points where the equations intersect.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they are the same line, there are infinitely many solutions.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

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 slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a linear equation?

Back

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

Front

What is a linear relationship?

Back

A relationship between two variables that can be represented by a straight line on a graph.

Front

How can you tell if a relationship is linear from a table of values?

Back

If the differences between consecutive y-values are constant for equal differences in x-values, the relationship is linear.

Front

What is the solution to a system of equations graphically?

Back

The solution is the point(s) where the graphs of the equations intersect.

Front

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

Back

It means the equations represent parallel lines that never intersect.