Solving Systems of Equations

Front

What is the solution to a system of equations?

Back

The solution (x, y) is the point where the equations intersect.

Front

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

Back

It means the two lines represented by the equations are intersecting lines.

Front

How many solutions can a system of linear equations have?

Back

A system can have one solution, infinitely many solutions, or no solution.

Front

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

Back

The lines are coincident, meaning they lie on top of each other.

Front

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

Back

The lines are parallel and never intersect.

Front

What is the solution to the system of equations represented by the point (1, -1)?

Back

The point (1, -1) is the intersection of the two lines in the system.

Front

If Lesly graphed two lines and found the solution (-3, -8), what does this point represent?

Back

It represents the point where the two lines intersect, which is the solution to the system.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if two lines are parallel from their equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.