Solving Systems of Equations

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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 it mean to solve a system of equations by substitution?

Back

Solving a system of equations by substitution 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 first step in solving a system of equations by substitution?

Back

The first step is to isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you check if a solution is correct for a system of equations?

Back

To check if a solution is correct, substitute the values of the variables back into the original equations to see if they hold true.

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What is the graphical interpretation of a system of equations?

Back

The graphical interpretation of a system of equations is the point(s) where the graphs of the equations intersect, representing the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the difference between consistent and inconsistent systems of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Tags

CCSS.8.EE.C.8B

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 other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the coefficients in a system of equations?

Back

The coefficients determine the slope and position of the lines represented by the equations, affecting the number of solutions.

Tags

CCSS.8.EE.C.8B

Front

How can you identify a system of equations with no solution?

Back

A system of equations has no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

Tags

CCSS.8.EE.C.8A