Systems of Linear Equations - All Methods

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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

What does it mean to solve a system of equations using substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting 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

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the solution to a system of equations?

Back

The solution represents 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 does it mean if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you set up equations from word problems?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure they reflect the problem's context.

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CCSS.HSA.CED.A.3

Front

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

Back

Isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

Align the equations and manipulate them (if necessary) to have the same coefficient for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6