Solutions to Graphs of Systems of Linear Equations

Front

What is a solution to a system of linear equations?

Back

A solution is a set of values for the variables that makes all equations in the system true.

Front

What does it mean if two lines intersect at a point on a graph?

Back

It means that the system of equations has one unique solution at that point.

Front

What does it mean if two lines are parallel on a graph?

Back

It means that the system of equations has no solution, as the lines never intersect.

Front

What does it mean if two lines coincide on a graph?

Back

It means that the system of equations has infinitely many solutions, as every point on the line is a solution.

Front

How can you determine the solution of a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What is the graphical representation of the equation y = 2x + 3?

Back

A straight line with a slope of 2 and a y-intercept of 3.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

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