Solving Systems of Equations

Front

What does the graph of a system of equations with no solution look like?

Back

Parallel lines.

Front

How many solutions does a system of equations with no solution have?

Back

No solution.

Front

Solve for x and y: 2x − 3y = −1 and y = x − 1.

Back

(4, 3)

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

Two overlapping lines.

Front

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

Back

(1, 3)

Front

What are the possible types of solutions for a system of equations?

Back

No solution, One solution, Infinitely many solutions.

Front

What does it mean if two lines are skew?

Back

They do not intersect and are not parallel.

Front

How can you determine if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What is the substitution method in solving systems of equations?

Back

Solving one equation for one variable and substituting it into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.