Graphing Systems of Equations

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?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

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

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect.

Front

What is the solution to the system of equations y = 6x - 4 and y = -x + 3?

Back

(1, 2)

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, so every point on the line is a solution.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line.

Front

What is the y-intercept in the equation y = mx + b?

Back

The value of y when x = 0, represented by b.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope.