Question

The sum of two numbers is 12, and their differences is 4 .write and solve a system of equations to find the value of the two numbers.

Answer 1

let the numbers are x and y

The sum of the numbers is 12

So, x + y = 12

the difference between the numbers is 4

So, x - y = 4

The system of equation will be:

$\begin{gathered} x+y=12\rightarrow(1) \\ x-y=4\rightarrow(2) \end{gathered}$

Add the equations to cross y then solve for x

$\begin{gathered} (x+y)+(x-y)=12+4 \\ x+y+x-y=12 \\ 2x=16 \\ x=\frac{16}{2}=8 \end{gathered}$

substitute with x into equation 1 to find y

$\begin{gathered} 8+y=12 \\ y=12-8 \\ y=4 \end{gathered}$

so, the answer will be the numbers are 8 and 4