H. Alg II Chap 3 CFA #3

Front

What is the elimination method in 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 does it mean if a system of equations has no solutions?

Back

It means that the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations. If they are the same, there are infinitely many solutions; if they are different, there is one solution; if they are parallel, there are no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

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

Solve the system of equations using elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

Solve the system of equations using substitution: y = 2x + 3 and y = -x + 1.

Back

(1, 5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you graph a system of equations?

Back

By plotting the lines represented by each equation on the same coordinate plane and identifying their points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

It means they have the same slope but different y-intercepts, resulting in no points of intersection.

Tags

CCSS.8.EE.C.8B