Systems Flashcard

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

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

Back

It means there is no solution to the system because the lines never intersect.

Front

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

Back

It means there are infinitely many solutions because every point on the line is a solution.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

It means there is exactly one solution to the system, which is the point of intersection.

Front

How do you solve a system of equations using substitution?

Back

You solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

You add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

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 y = 4x + 1 and 3x + 2y = 13?

Back

(1, 5)

Front

If the equations of two lines are 6x + y = 26 and y = 2x + 10, what is the value of y when x = 2?

Back

14