Question

$$\begin{gathered} \mathrm{\_}+\mathrm{\_}=17 \\ ++ \\ \mathrm{\_}-\mathrm{\_}=13 \\ == \\ 1915 \end{gathered}$$

Answer 1

Step 1: Given information

$$\begin{gathered} \mathrm{\_}+\mathrm{\_}=17 \\ ++ \\ \mathrm{\_}-\mathrm{\_}=13 \\ == \\ 1915 \end{gathered}$$

Step 2: Determine the characteristic equation

Consider the variables $x,y,a,b$

$$\begin{gathered} \mathrm{x}+\mathrm{y}=17 \\ \mathrm{a}-\mathrm{b}=13 \end{gathered}$$

We get,

$$\begin{gathered} \mathrm{x}+\mathrm{y}=17 \\ ++ \\ \mathrm{a}-\mathrm{b}=13 \\ == \\ 1915 \end{gathered}$$

Step 3: To determine the value of $\mathrm{x}\mathrm{and}\mathrm{y}$

So, we have,

$$\begin{gathered} \mathrm{x}+\mathrm{y}=17 \\ \mathrm{y}+\mathrm{b}=15 \end{gathered}$$

Isolate the $\mathrm{y}$ for $\mathrm{y}+\mathrm{b}=15$ we get, $\mathrm{y}=15-\mathrm{b}$

Substitute the value in above equation

$\mathrm{x}+(15-\mathrm{b})=17$

$\mathrm{x}-\mathrm{b}=2------\left(1\right)$

So, we have,

$$\begin{gathered} \mathrm{x}+\mathrm{a}=19 \\ \mathrm{a}-\mathrm{b}=13 \end{gathered}$$

Isolate the $\mathrm{x}$ for $a-b=13$ we get, $a=13+b$

Substitute the value in above equation

$\mathrm{x}+(13+b)=19$

$\mathrm{x}+\mathrm{b}=6------\left(2\right)$

Step 3: To add equations $\left(1\right)$ and $\left(2\right)$

$$\begin{gathered} \mathrm{x}-\mathrm{b}=2...\left(1\right) \\ \mathrm{x}+\mathrm{b}=6...\left(2\right) \end{gathered}$$

$$\begin{gathered} \Rightarrow 2\mathrm{x}=8 \\ \Rightarrow \mathrm{x}=4 \end{gathered}$$

We can find the values of y, a and b by substituting the obtained value of x.

so, we get,

$\mathrm{x}=4,\mathrm{y}=13,\mathrm{a}=15$ and $\mathrm{b}=2$

But the given problem is wrong.

Hence,The correct form is,

$$\begin{gathered} 4+\; 13\; =\; 17 \\ ++ \\ 15–\; 2\; =\; 13 \\ == \\ 1915 \end{gathered}$$