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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for solving systems of equations?

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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 determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

A system has one solution if the lines intersect at a single point, no solution if the lines are parallel, and infinitely many solutions if the lines coincide.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane; the points of intersection represent the solutions.

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 isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

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

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 by substituting the solution back into the original equations to see if both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, resulting in infinitely many solutions.

Tags

CCSS.8.EE.C.8B