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 to 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 a y-intercept?

Back

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

Front

How do you find the y-intercept of a linear equation?

Back

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

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

What does it mean if two lines are parallel?

Back

They have the same slope and will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Their slopes are negative reciprocals of each other, meaning they intersect at a right angle.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are satisfied, it is a solution.

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line with slope 'm' and y-intercept 'b'.