Warm-Up 11/6-11/7

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What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing you to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of linear equations to have a unique solution?

Back

A unique solution means that the two lines represented by the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of linear equations?

Back

The graphical representation consists of two lines on a coordinate plane, where the solution is the point of intersection.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if a system of equations has no solution?

Back

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

Tags

CCSS.8.EE.C.8A

Front

How do you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the two equations represent the same line, meaning they have the same slope and y-intercept.

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

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

Back

The first step is to align the equations and manipulate them (if necessary) to make the coefficients of one variable the same.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

The solution is (1, 3), where both equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution.

Tags

CCSS.8.EE.C.8B