Systems of Equations

You can solve a system of equations be adding or subtracting the equations in such a way that one variable drops out. This is called the ____ method.

• elimination

• substitution

• graphing

Answer explanation

In elimination, you use properties of equality to add or subtract equations to eliminate a variable in a system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Any ordered pair that makes all of the equations in a system true.

• System of linear equation

• solution of a system of linear equations

• elimination method

• substitution method

Answer explanation

Any ordered pair that makes all of the equations in a system true is a solution to a system of linear equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

A group of students on a field trip. If the group takes 3 vans and 1 car, 22 students can be transported. If the group takes 2 vans and 4 cars, 28 students can be transported. How many students can fit in each van?

Answer explanation

Read the problem, underline and write important keywords. Set a system of linear equations using the given information.

Tags

CCSS.8.EE.C.8C

What is the solution for the following system of equations?

5x + 7y =3

2x + 3y =1

• (-2, 1)

• (2, -1)

• (1, -2)

• (-1, 2)

Answer explanation

To solve systems of equations either use the graphing, substitution, or elimination method.

Write answered in ordered pair (x, y).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following of equations using elimination. What is the value of y?

2x + 3y =105

x + 2y = 65

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Can a system of two linear equations have exactly two solutions? Explain

Answer explanation

Two lines intersect in no points, one point, or an infinite number of points .

Tags

CCSS.8.EE.C.8B

Which best describes a system of equations that has no solution?

• consistent, independent

• inconsistent, dependent

• consistent, dependent

• inconsistent

Answer explanation

A system of equations that has no solution is inconsistent.

Tags

CCSS.8.EE.C.8B

Solve the system and tell whether the system has one solution, infinitely many solutions, or no solutions.

18x - 3y =21

-y = -6x + 7

• one solution

• no solution

• infinitely many solutions,

Tags

CCSS.8.EE.C.8B

A snack bar sells two sizes of snack packs. A large snack pack is $5, and a small snack pack is $3. In one day, the snack bar sold 60 snack packs for a total of $220. How many small snack packs did the snack bar sell?

• (20, 40)

• (60, 220)

• (25, 35)

• (10, 30)

Answer explanation

Write the system of equations. Let x = the number of large $5 snack packs, and let y = the number of small $3 snack packs.

Tags

CCSS.8.EE.C.8C

Systems of equations can be solved in more than one way either by graphing, substitution, or elimination, which method do you prefer?

(a)  

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6