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 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

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?

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The graphical interpretation involves plotting the equations on a coordinate plane; the point(s) where the lines intersect represent the solution(s) of the system.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines indicate that the system has no solution, as the lines never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two equations represent the same line?

Back

If two equations represent the same line, the system has infinitely many solutions, as every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

Front

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

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you identify which method (substitution or elimination) to use for solving a system of equations?

Back

The choice of method can depend on the structure of the equations; use substitution if one equation is easily solvable for a variable, and use elimination if the coefficients are conducive to cancellation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

Coefficients are the numerical factors in front of the variables; they affect the slope and position of the lines represented by the equations.

Tags

CCSS.8.EE.C.8A