How do you solve the system \[x+y=15\] and \[x-y=-19\]?

Hint: To solve the system of equations in two variables, we need to follow the steps given below in the same order:
Step 1: choose one of the equations to find the relationship between the two variables. this can be done by taking one of the variables to the other side of the equation.
Step 2: substitute this relationship in the other equation to get an equation in one variable.
Step 3: solve this equation to find the solution value of the variable.
Step 4: substitute this value in any of the equations to find the value of the other variable.

Complete step by step answer:
We are given the two equations \[x+y=15\] and \[x-y=-19\]. We know the steps required to solve a system of equations in two variables. Let’s take the first equation, subtracting \[x\]from both sides of this equation, we get
\[\Rightarrow y=15-x\]
Substituting this in the equation \[x-y=-19\], we get
\[\Rightarrow x-\left( 15-x \right)=-19\]
Simplifying the above equation, we get
\[\Rightarrow 2x=-4\]
Dividing both sides by 2, we get
\[\begin{align}
  & \Rightarrow \dfrac{2x}{2}=\dfrac{-4}{2} \\
 & \therefore x=-2 \\
\end{align}\]
Substituting this value in the first equation, we get
 \[\Rightarrow -2+y=15\]
Solving the above equation, we get
\[\therefore y=17\]

Hence, the solution values for the system of equations are \[x=-2\And y=17\].

Note: We can check if the solution is correct or not by substituting the values we got in the given equations. Substituting \[x=-2\And y=17\] in the first equation, \[LHS=17+(-2)=17-2=15=RHS\]. Substituting \[x=-2\And y=17\] in the second equation, \[LHS=-2-17=-19=RHS\]. Hence, as both equations are satisfied the solution is correct.