Systems of Equations by Graphing, Substitution, Adding or Subtracting

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.

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).

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

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OFF

Answer explanation

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

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.

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

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

2x + 3y =105

x + 2y = 65

a method used to solve systems of equations by graphing the equations and looking for points of intersection

• substitution method

• graphing method

• elimination method

a system with at least one solution

• consistent system

• inconsistent system

• independent system

• dependent system

a system that has no solution

• consistent system

• inconsistent system

• independent system

• dependent system

a system that has infinitely many solutions

• consistent system

• inconsistent system

• independent system

• dependent system