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 when two lines intersect on a graph?

Back

The point of intersection represents the solution to the system of equations.

Front

What is the solution to a system of equations when the lines are parallel?

Back

No solution, as parallel lines never intersect.

Front

What does it mean when two lines are graphed over each other?

Back

Infinitely many solutions, as every point on the line is a solution.

Front

How do you find the y-intercept of a line?

Back

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

Front

What is the y-intercept of the equation y = 2x + 1?

Back

1, as it is the value of y when x = 0.

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 (x1, y1) and (x2, y2)?

Back

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

Front

What is the graphical representation of the equation y = -3x + 4?

Back

A straight line with a slope of -3 and a y-intercept of 4.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.