Three Variable Systems of Equations

A local grocery store makes a 9-pound mixture of trail mix. The trail mix contains raisins, sunflower seeds, and chocolate-covered peanuts. The raisins costs $2 per pound, sunflower seeds cost $1 per pound, and chocolate-covered peanuts cost $1.50 per pound. The total cost for the mixture is $14.50. Set up the system of equations using the following:

The solution of a system of three linear equations in three variables, x,y, and z, is called a(n) ___________________ (x,y,z).

• Ordered Pair

• Integer

• Ordered Triple

• Sum

What is your solution if your variables go away and you are left with 0 = 0?

• No Solution

• All Real Numbers

• Infinitely Many Solutions

• (x, y, z)

How confident do you feel solving linear systems in three variables?

• Very confident, and could help a friend.

• Fairly confident, but would like more practice

• Somewhat confident, but have some questions

• Not confident yet, and would like some help

Solve this system of equations:

x+2y-z=10

y+z=5

2z=4

• (14,3,2)

• (-2,7,2)

• (6,3,2)

• (12,1,4)

Solve the system of equations:

2x+4y-z=4

x+2y-3z=-8

3x-y+z=2

• (4,0,2)

• (0,2,4)

• (4,-8,2)

• (-8,2,4)

The solution to a 3-variable systems of equation is...

• the intersection of three planes

• the origin

• infinitely many solutions

• no unique solution

Solve the system.

• (1, 2, -5)

• (1, -2, 5)

• (2, -4, -5)

• (3, 1, -5)

Is (4,5,6) a solution to 2x-3y+z=8

• Yes

• No

What is your solution if your variables go away and you are left with 0 = 0?

• No solution

• Infinitely many solutions

• All real numbers

• (x,y,z)