x+y=7 y+z=9 z+t=13 what is the value of x+t?

Question

X+Y=7

Y+Z=9

Z+T=13

What is the value of X+T?

Please show and explain your answers. This question is from the Clep study guide.

Answer 1

Quickest way:

X+T = (X+Y) - (Y+Z) + (Z+T) = 7 - 9 + 13 = 11.

Answer 2

X+T=11

With simple equations, you can learn a lot about them through some quick value substitution.

Easiest is to set the first variable to 0 & calculate the possible values of the remaining variables.

For X=0, Y=7, Z=2, T=11. Therefore, X+T=11.

To verify:

For Y=0, X=7, Z=9, T=4.

For Z=0, Y=9, X=-2, T=13.

For T=0, Z=13, Y=-4, X=11.

In all cases, X+T must equal 11.

Answer 3

Since z + t = 13, z = 13 - t

Since y + z = 9, y + (13 - t) = 9

So, y - t = -4

Since x + y = 7, y = 7 - x

So, (7 - x) - t = -4

x + t = 11