Question

How do you solve \[x - y = 5\] and \[x + y = 3\] ?

Answer 1

Hint: These are linear equations with two variables. We will solve this simply by elimination method because the sign of another variable is opposite to the sign of the same variable in the first equation. On adding them one will be eliminated giving the value of the other. Then assigning the value of this obtained variable in any of the equations we can get the value of the remaining one.

Complete step-by-step answer:
Given that,
\[x - y = 5....equation1\]
\[x + y = 3....equation2\]
On adding the equation above,
\[x - y + x + y = 5 + 3\]
Now we can see y will be eliminated automatically and then we will add the same variables on one side and constants on other side,
\[2x = 8\]
On dividing by 2 on both sides we get,
\[x = 4\]
This is the value of one of the variables. Now we will put this value in equation1 and find the value of y.
\[4 - y = 5\]
Taking constants on one side,
\[4 - 5 = y\]
\[y = - 1\]
This is the value of the second variable.
Thus the solution of the equation is x=4 and y=-1
So, the correct answer is “ x=4 and y=-1”.

Note: Here note that there is no necessity of fusing any other methodology like substitution or any other complicated things. Because the coefficients of both the variables are 1. So no need to make them maintain the same variable. So we directly used the elimination method. If these things are only there then first we will do them like making the coefficients of the cancelling variable same and then we will proceed but only in elimination method.