Systems of Linear Equations

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What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. Solutions are the points where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the three methods to solve a system of linear equations?

Back

1. Graphing 2. Substitution 3. Elimination

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of linear equations?

Back

The lines representing each equation on a coordinate plane, where the intersection point(s) represent the solution(s).

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of linear equations has no solution?

Back

The lines are parallel and do not intersect, indicating that there are no values that satisfy all equations.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of linear equations has an infinite number of solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

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How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

Front

What is the substitution method for solving systems of equations?

Back

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

What is the elimination method for solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you represent a system of equations using matrices?

Back

By creating a coefficient matrix and a constant matrix, which can be solved using matrix operations.

Tags

CCSS.HSA.REI.C.8