Solving Systems of Equations using Elimination

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does elimination mean in the context of solving systems of equations?

Back

Elimination is a method used to solve systems of equations by removing one variable, allowing for the solution of the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you eliminate a variable in a system of equations?

Back

To eliminate a variable, you can add or subtract the equations in such a way that one variable cancels out.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in using elimination to solve a system of equations?

Back

The first step is to align the equations so that the coefficients of one variable are opposites or can be made opposites.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude?

Back

The two equations represent the same line, so there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the importance of checking your solution after solving a system of equations?

Back

Checking your solution ensures that the values satisfy all equations in the system, confirming that the solution is correct.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What happens if you eliminate the wrong variable in a system of equations?

Back

Eliminating the wrong variable can lead to incorrect solutions or no solution at all.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Tags

CCSS.8.EE.C.8A

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines.

Tags

CCSS.8.EE.C.8A