# System of Three Equations

Pro Problems > Math > Algebra > Equations > Systems of Equations## System of Three Equations

Find the ordered triple (x, y, z) if x + y + z = 16; x - z = 10; and y + z = 9

Presentation mode

Problem by BogusBoy

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.Assign this problem

Click here to assign this problem to your students.## Similar Problems

### Find X + Y + Z

If 2X + 3Y + 4Z = 100 and 5X + 7Y + 9Z = 242, find X + Y + Z.

### System of Equations with K

The following is a system of equations in x and y, with a constant K.

x + 2y = K

x - y = 2

If K is an integer between 20 and 25 inclusive, find all K such that the system has integer solutions.

### P and Q

The sum of p and q is 44. q is two more than twice p. Find the ordered pair (p, q).

### Ugly Fractional System

Find the ordered pair (m,n) which solves the following system of equations.

2(-19

2

1

4

9

2

### P and Q

p is 12 more than a third of q, which is 12 less than half of p. Find the ordered pair (p, q)

### b Over X + Y

The sum of two numbers is X.

^{2}, and their difference is Y^{2}. X is 4 more than Y. If the smaller of the two numbers is b, calculateb

X + Y

### Three to Two

If 3x + 5y + z = 100, and 2z + 7x + 9y = 56, find the value of

y - x

.### System in a System

3x + 4y = 16

2x - 2y = 6

Also,

xm + yn = 28

ym + xn = 22

Find the ordered pair (m, n).

### Fractions within Fractions

Find all ordered pairs (x,y) such that:

1 + + -

2

x

1

x

^{2}4

y

^{2}1 + +

1

x

2

y

1 + + -

2

x

1

x

^{2}4

y

^{2}1 + -

1

x

2

y

# Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!**Get a**

*FREE*Pro-Membership!Educators can get a free membership simply by sharing an original lesson plan on our

*Articles for Educators*page!

Like us on Facebook to get updates about new resources