Solving Systems of Equations - algebra 1

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Tags

CCSS.8.EE.C.8B

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

Back

It is the visual depiction of the equations on a coordinate plane, where the solutions are the points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two equations in a system are identical?

Back

It means they represent the same line, resulting in infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By substituting the solution back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations so that like terms are in the same column, making it easier to eliminate a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6