Solving Systems of Equations

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 solution to the system of equations represented by the lines y=8x+1 and y=6x+3?

Back

(1, 9)

Front

What type of lines represent a system of equations with no solution?

Back

Parallel lines.

Front

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

Back

The two lines are the same line.

Front

How can you solve a system of equations using substitution?

Back

Replace one variable with an expression from another equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.

Front

If two lines intersect at a point, how many solutions does the system have?

Back

One solution.

Front

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

Back

Two parallel lines.

Front

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

Back

One line on top of another.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

Analyze the slopes and y-intercepts of the lines.