Question

Find the two numbers their sum is -7 and their difference is 14.

Answer 1

Answer:

The two numbers are  3$\frac{1}{2}$  and -10$\frac{1}{2}$

Step-by-step explanation:

To find the two numbers whose sum is -7 and whose difference is 14, we will do the following;

we will first represent  the statement mathematically.

let x and y be the two numbers respectively.

"The sum of the two numbers is -7" can be represented mathematically as;

x + y = -7 -----------------------------------------(1)

"Their difference is 14" can be represented mathematically as;

x - y = 14 ------------------------------------------(2)

Next is to solve the two equation simultaneously

We will use both elimination and substitution method to solve the system of the equation

lets add equation (1) and equation (2) together

2x = 7

Divide both-side of the equation by 2

2x/2 = 7/2

x = $\frac{7}{2}$

x = 3$\frac{1}{2}$

Substitute x =   $\frac{7}{2}$ in  equation (1)

x + y = -7

$\frac{7}{2}$ + y = -7

Subtract $\frac{7}{2}$ from both-side of the equation

$\frac{7}{2}$ - $\frac{7}{2}$ + y = -7  - $\frac{7}{2}$

y   = $\frac{-14-7}{2}$

y = $\frac{-21}{2}$

y =-10$\frac{1}{2}$

The two numbers are  3$\frac{1}{2}$  and -10$\frac{1}{2}$

Answer 2

Answer:

b = -10.5, a = 3.5

Step-by-step explanation:

Step 1:  Convert words into an expression

Find the two numbers their sum is -7 and their difference is 14.

a + b = -7

a - b = 14

Step 2:  Solve for a in the first equation

a + b - b = -7 - b

a = -7 - b

Step 3:  Find the b in the second equation

a - b = 14

(-7 - b) - b = 14

-7 - 2b + 7 = 14 + 7

-2b / -2 = 21 / -2

b = -10.5

Step 4:  Substitute into a

a = -7 - b

a = -7 - (-10.5)

a = -7 + 10.5

a = 3.5

Answer:  b = -10.5, a = 3.5