Question

The sum of two integers is 10. Their difference is 4. What arethe two integers?

Answer 1

the numbers are 7 and 3

Explanation

Step 1

Let x represents integer1

let y represetns integer2

The sum of two integers is 10

replace

$x+y=10\Rightarrow equation(1)$

Their difference is 4.

$x-y=4\Rightarrow equation(2)$

Step 2

to solve, isolate x in equation (1) and replace in equation(2)

$\begin{gathered} x+y=10\Rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=10-y \\ x=10-y \\ \text{replace in equation(2)} \\ x-y=4\Rightarrow equation(2) \\ (10-y)-y=4 \\ 10-2y=4 \\ \text{subtratc 10 in both sides} \\ 10-2y-10=4-10 \\ -2y=-6 \\ \text{divide both sides by -2} \\ \frac{-2y}{-2}=\frac{-6}{-2} \\ y=3 \end{gathered}$

now, replace in equation (1)

$\begin{gathered} x+y=10\Rightarrow equation(1) \\ x+3=10 \\ \text{subtract 3 in both sides} \\ x+3-3=10-3 \\ x=7 \end{gathered}$

so, the numbers are 7 and 3