# -2t-u=-2 -10-u=-6 8t+u=5 What is the value of t and u?

The equations are literally screwed. Use all three different ways to solve and you will get different answers.

#### Explanation:

You can literally get the answer using only two of the three equations above. I'm going to use elimination and eliminate $u$ for everything. HOWEVER, ALL OF THE ANSWERS WILL BE DIFFERENT, THE EQUATIONS THEMSELVES ARE SCREWED, I CHECKED ABOUT 5 TIMES AND I DID NOTHING WRONG.

Way 1
$- 2 t - u = - 2$
$- 10 - u = - 6$
Eliminate $u$ by subtracting.
$- 10 + 2 t = - 4$
$2 t = 6$
$t = 3$

Way 2
$- 2 t - u = - 2$
$8 t + u = 5$
Eliminate $u$ by adding. (Here, it is also possible to eliminate $t$... but it's easier to subtract $u$.)
$6 t = 3$
$t = 0.5 = \frac{1}{2}$

Way 3
$- 10 - u = - 6$
$8 t + u = 5$
Eliminate $u$ by adding.
$8 t - 10 = - 1$
$8 t = 9$
$t = \frac{9}{8} = 1 \frac{1}{8} = 1.125$

May 20, 2018

There is no values of t and u which fulfill all three equations at the same time.

#### Explanation:

I hope you mean as follows:
1) $- 2 t - u = - 2$
2) $- 10 - u = - 6$
3) $8 t + u = 5$
As you have three equations and only two unknowns, you risk this to be overdefined, i.e. that there are no values of t and u that will fulfill all three equations, so we are on dangerous grounds here.

Therefore, let's see what happens when we try to solve this.

Equation 1): $- 2 t - u = - 2 \implies 2 t + u = 2$
This gives $t = 1 - \frac{u}{2}$

2): $- 10 - u = - 6 \implies 10 + u = 6 \implies u = - 4$

Insert in 1): $t = 1 - \left(- \frac{4}{2}\right) = 1 + 2 = 3$

Does this fit into 3)?
$8 t + u = 8 \cdot 3 - 4 = 24 - 4 = 20 \ne 5$
Conclusion t=3, u=-4, which solved 1) and 2), does not fit equation 3.

Another way of testing this is to draw a graph of all three equations and see if the three graphs cross in one point. As the graph below shows, this is not the case. Therefore, there is no values of t and u which fulfill all three equations at the same time - only two and two equations in pairs: