Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations graphically?

Back

It means to find the point(s) where the graphs of the equations intersect, representing the solution(s) to the system.

Front

What is the solution to the system of equations: y = -3x + 4 and 3x + 2y = 8?

Back

(0, 4)

Front

How do you represent a system of equations with two variables?

Back

Using two equations, such as: n + q = 15 and 0.05n + 0.25q = 2.35.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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, as the lines never intersect.

Front

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

Back

It means there are infinitely many solutions, as the lines overlap completely.

Front

What is an ordered pair in the context of systems of equations?

Back

A pair of numbers (x, y) that represents a point on the coordinate plane, which is a potential solution to the system.

Front

How can you check if an ordered pair is a solution to a system of equations?

Back

By substituting the values of the ordered pair into both equations to see if they hold true.