Systems of Equations --- Substitution

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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 set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does substitution mean in the context of solving systems of equations?

Back

Substitution is a method for solving a system of equations by 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

How do you solve a system of equations using substitution?

Back

1. Solve one of the equations for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find 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 point (or points) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations consists of the lines or curves of the equations plotted on a coordinate plane, where the intersection points represent the solutions.

Tags

CCSS.HSA.REI.C.7

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations is one that has no solution, meaning the lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is a dependent system of equations?

Back

A dependent system of equations is one that has infinitely many solutions, meaning the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

What is an independent system of equations?

Back

An independent system of equations is one that has exactly one solution, meaning the lines representing the equations intersect at a single point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

You can check your 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 first step in solving the system: y = 3x - 8 and y = 4 - x?

Back

The first step is to set the two expressions for y equal to each other: 3x - 8 = 4 - x.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6