Find the Variable

Question

1. XY=11, YZ=4c, XZ=83--- C= ??
2. XY=7a, YZ=5a, XZ=6a + 24--- YZ=??
3. XY=4n +3, YZ=2n -7, XZ=22--- N= ??

Answer 1

Draw and label diagrams!

XY + YZ = XZ

1.

11 + 4c = 83

Solve for c

2.

7a + 5a = 6a _ 24

Solve for a

3.

(4n + 3) + (2n - 7) = 22

Solve for n

Answer 2

1. XY=11, YZ=4c, XZ=83--- C= ??

XY + YZ = XZ

11 + 4c = 83

4c = 72

c = 18

1. XY=7a, YZ=5a, XZ=6a + 24--- YZ=??

7a + 5a = 6a + 24

6a = 24

a = 4

YZ = 5a = 20

1. XY=4n +3, YZ=2n -7, XZ=22--- N= ??

4n+3 + 2n - 7 = 22

6n - 4 = 22

6n = 26

n = 13/3

Answer 3

In all 4 of these, there are 4 unknowns but only three equations.

So that means you must declare a free variable

(1) Free variable is y

C = (yz)/4 per 2nd equation

(83/z)y = 11 <--- solves 3rd equation for x and substitutes

into first equation.

83y = 11z

(83/11)y = z <-- substitutes into above equation

C = ( 83/44) y^2