8.9A Simultaneous 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.

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.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

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The intersection point(s) of the lines representing the equations on a graph.

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CCSS.8.EE.C.8A

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What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

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(1, 3)

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving linear equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving linear equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.

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CCSS.8.EE.C.8B

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

Back

The system has infinitely many solutions because the lines are the same.

Tags

CCSS.8.EE.C.8A

Front

What is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the importance of the coefficients in a linear equation?

Back

They determine the slope and position of the line on a graph.

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CCSS.8.EE.B.6

CCSS.8.F.A.3