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 intersection point(s) of the lines representing the equations.

Front

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

Back

(1, 3)

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

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

Back

They have the same slope and will never intersect.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the solution to the system of equations 3x - y = 7 and 2x + y = 3?

Back

(2, -1)

Front

What is the meaning of the y-intercept in a linear equation?

Back

The point where the line crosses the y-axis (x=0).

Front

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

Back

If the lines are parallel, they do not intersect.