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 for a system of equations to be consistent?

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A consistent system of equations has at least one solution. It can be either a unique solution or infinitely many solutions.

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CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions, meaning the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8B

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What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection point(s) of the lines represented by the equations on a coordinate plane.

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CCSS.8.EE.C.8B

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What is the substitution method for solving systems of equations?

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The substitution method 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

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How do you determine if two lines are parallel?

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Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Tags

CCSS.8.EE.B.6

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the point of intersection of two lines?

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The point of intersection of two lines is the solution to the system of equations, representing the values of the variables that satisfy both equations.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you check the solution of a system of equations?

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You can check the 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