Set Up Systems of Equations

________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Answer explanation

The lines intersect at (1,3) so that is the solution.

Will the solution (-3, -7) make the following system of equations a true statement?

• YES

• NO

Answer explanation

Which variable would be easiest to eliminate?

• x

• y

• Neither

Answer explanation

The terms with x in them have opposite coefficients (4x and -4x), so they will be the easiest to eliminate when we add the equations together.

Solve the following using elimination.

• (10,-1)

• (-1,10)

• (-1,-10)

• (-10,-1)

Answer explanation

7x - y = 10

-7x + y = -14

• No Solution

• (4, 1)

• Infinitely Many Solutions

• (2, -4)

Answer explanation

7x - y = 10

-7x + y = -14

All of the like terms have opposite coefficients, so both variables will be eliminated when we add the equations together. We cannot eliminate one without the other.

We are left with:

0=-4

This is a contradiction (false), so there is NO SOLUTION.

Homer sells tickets for admission to the school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets.

• a + c = 21

  6a + 4c = 104

• a + c = 104

  6a + 4c = 21

• a + c = 21

  6c + 4a = 104

• a + c = 104

  6c + 4a = 21

Enterprise charges to rent compact cars for a fixed amount per day plus a fixed amount for each mile driven. Batman rented a car for 6 days, drove it 550 miles and spent $337. Superman rented the same car for 3 days, drove for 350 miles and spent $185. Set up the system. Let "d" represent the fixed charge per day and "m" represent the cost per mile.

• 6d + 550m = 337

  3d + 350m = 185

• 6d + 550m = 185

  3d + 350m = 337

• 6m + 550d = 337

  3m + 350d = 185

• 6m + 550d = 185

  3m + 350d = 337

The sum of twice a number x and three times a number y is 69. The different between four times number x and twice number y is 18. What are the numbers x and y?

• 2x + 3y = 69 and 4x - 2y = 18

  x = 15 and y = 12

• 3x + 2y = 69 and 4x - 2y = 18

  x = 16 and y = 12

• 2x + 3y = 69 and 4x - 2y = 18

  x = 12 and y = 15

• 3x - 2y = 69 and 4x + 2y = 18

  x = -16 and y = 12

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist