Solving Systems of Equations

Front

What does the graph of a system of equations with infinitely many solutions look like?

Back

The same line (coinciding lines)

Front

How many solutions does a system of equations have if the lines are parallel?

Back

No solution

Front

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

Back

(0,4)

Front

Is (1,7) a solution for the system y=3x+4 and y=x+6?

Back

Yes

Front

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

Back

The lines intersect at exactly one point.

Front

What is the graphical representation of a system with no solutions?

Back

Parallel lines that never intersect.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations and check if both are true.

Front

What is a system of equations?

Back

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

Front

What does it mean for two lines to be skew?

Back

They do not intersect and are not parallel, existing in different planes.

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.