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What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear 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

How can you represent a solution to a system of linear equations?

Back

A solution to a system of linear equations with two variables is represented as an ordered pair (x, y).

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CCSS.HSA.REI.C.9

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What does it mean for a solution to satisfy a system of equations?

Back

A solution satisfies a system of equations if it makes all equations in the system true when the values of x and y are substituted.

Tags

CCSS.HSA.REI.C.9

Front

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

Back

The graphical representation of a system of linear equations consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s).

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for solving systems of linear equations?

Back

The substitution method involves solving one equation for one variable and then substituting 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 linear equations?

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 does it mean if two lines are parallel in the context of a system of linear equations?

Back

If two lines are parallel, it means that the system of equations has no solution, as the lines never intersect.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines coincide in the context of a system of linear equations?

Back

If two lines coincide, it means that the system of equations has infinitely many solutions, as every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

What is the importance of checking solutions in a system of linear equations?

Back

Checking solutions 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

How do you determine if a system of equations is consistent or inconsistent?

Back

A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.

Tags

CCSS.8.EE.C.8B