Ch 5 Review: Solving Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for two lines to intersect in a graph?

Back

When two lines intersect, it means they have one solution, which is the point where they cross.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, they never intersect and have no solutions.

Front

What does it mean if two lines are coincident?

Back

If two lines are coincident, they lie on top of each other and have infinitely many solutions.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What must be true about the coefficients of the eliminated variable in the elimination method?

Back

The coefficients of the eliminated variable must be the same number with opposite signs.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

Front

What is the graphical representation of a system with one solution?

Back

A system with one solution is represented by two lines that intersect at a single point.

Front

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

Back

A system with infinitely many solutions is represented by two coincident lines that overlap completely.

Front

How can you check your solution to a system of equations?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.