Question

Solve the system of equations and choose the correct answer from the list of options.

d + e = 15
−d + e = −5

Label the ordered pair as (d, e).

(0,0)
(10,-5)
(5, 10)
(10, 5)

Answer 1

d + e = 15    ..... (i)

-d + e = -5  ........(ii)

From equation (i)

d + e = 15

e = 15 - d .......(iii)

Substitute (iii) into (ii)

-d + e = -5  ........(ii)
 
-d + 15 - d = -5

-d - d + 15 = -5

-2d =  -5 -15          -2d = -20.      Divide both sides by -2

-2d / -2  =  -20 / -2

d = 10

From (iii)  e = 15 - d

e = 15 - 10 = 5.

(d , e ) =  (10 , 5).

Fourth option is the answer.

Answer 2

d + e = 15
-d + e = -5

If we add both equations, we get:

d + (-d) + e + e = 15 + (-5)
2e = 10
e = 5

There is only one answer choice that has e =5, and that is (10,5).

Just to be sure, let's solve for d.

d + e = 15
d + 5 = 15
d = 10

Your answer is D. (10,5).