How do you solve this system of equations \[y - x = - 5,\,x + y = 8\]?

Hint: To solve any given set of linear equations of two variables, we need to eliminate one of the variable from both the equation with the help of mathematical operation in order to get the value for the non-eliminated variable, and once the value of one variable is obtained then by putting that value in the equation we can get the value for the other variable.

Complete step by step solution:
The given set of linear equations are \[y - x = - 5,\,x + y = 8\]
For solving this variable and getting the value of one of the variable after eliminating one variable, here we need to add both the equations, here we can see that after adding both the equation “x” variable is getting eliminated and we can get the value for the next variable, on solving we get:
\[
   \Rightarrow (y - x = - 5) + (x + y = 8) \\
   \Rightarrow y - x + x + y = - 5 + 8 \\
   \Rightarrow 2y = 3 \\
   \Rightarrow y = \dfrac{3}{2} \\
 \]
Now putting this value in the any of the equation we can get the value of the other variable, on solving we get:
\[
   \Rightarrow y - x = - 5 \\
   \Rightarrow y = \dfrac{3}{2} \\
   \Rightarrow \dfrac{3}{2} - x = 5 \\
   \Rightarrow x = - 5 + \dfrac{3}{2} \\
   \Rightarrow x = \dfrac{{ - 10 + 3}}{2} = \dfrac{{ - 7}}{2} \\
 \]
Here we get the values of the given two variables.

Note: In order to get the values of the variables, we need to solve the given equations, so that by eliminating one variable we can get the value of the other variable. Here we can solve this question, by plotting the graph for both the equation, and the intersection point of these two equations on graph will have the coordinate, and this coordinate will be the value of the given variables in the question.