Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution of a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What is the y-intercept of a graph?

Back

The point where the graph crosses the y-axis, represented as (0, y).

Front

How do you find the y-intercept from an equation?

Back

Set x = 0 in the equation and solve for y.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution, as the lines never intersect.

Front

What does it mean if two lines are coincident?

Back

It means they are the same line, resulting in infinitely many solutions.

Front

What is the slope of a line?

Back

The rate of change of y with respect to x, often represented as 'm' in the equation y = mx + b.

Front

How do you determine the slope from two points?

Back

Use the formula m = (y2 - y1) / (x2 - x1).

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.