Solving Systems of Equations

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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 are the three main methods for solving systems of equations?

Back

The three main methods are: 1) Graphing, 2) Substitution, 3) Elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is substitution the best method to solve a system of equations?

Back

Substitution is best when one equation is easily solvable for one variable, allowing for straightforward substitution into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to graph a system of equations?

Back

Graphing a system of equations involves plotting each equation on the same coordinate plane to visually identify the point(s) of intersection, which represent the solution.

Tags

CCSS.8.EE.C.8B

Front

How do you solve a system of equations using the elimination method?

Back

To use elimination, you manipulate the equations to eliminate one variable, allowing you to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the set of values for the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the point of intersection in a graph of two lines?

Back

The point of intersection represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

How can you check if a solution to a system of equations is correct?

Back

You can check a solution by substituting the values 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 elimination method?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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