Solving Systems of Equations

Front

What is the solution (x, y) to a system of equations?

Back

The point where the equations intersect.

Front

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

Back

The graphs of the equations are the same line (coinciding lines).

Front

What does it mean if a system of linear equations has one solution?

Back

The two lines intersect at one point.

Front

What is the graphical representation of parallel lines in a system of equations?

Back

The lines never intersect and have no solutions.

Front

How do you solve a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the intersection point.

Front

What is the solution to the system of equations: y=8x+1 and y=6x+3?

Back

(1, 9)

Front

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

Back

They do not intersect and are not parallel (only in 3D space).

Front

What is a system of equations?

Back

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

Front

What is the substitution method in solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.