Question

How do you solve 2x – y = 7 and 3x + y = 8?

Answer 1

We will first find the value of y from the given first equation and then put in this value of y in terms of x in the second equation to get the value of x.

Complete step-by-step answer:
We are given that we are required to solve the system 2x – y = 7 and 3x + y = 8.
Let us assume the equation as 2x – y = 7 ………………(1) (equation number 1)
And 3x + y = 8 ……………..(2) (equation number 2)
Now, we have two equations.
Considering first equation: 2x – y = 7
Taking y from subtraction in the left hand side to addition in right hand side, we will get the following equation:-
$\Rightarrow$2x = 7 + y
Taking 7 from addition in the right hand side to subtraction in left hand side, we will get the following equation:-
$\Rightarrow$y = 2x – 7
Now, putting this value of y in equation number (2), we will then get:-
$\Rightarrow$3x + (2x – 7) = 8
Simplifying the expression in the above equation by opening the bracket on the left hand side, we will obtain the following equation:-
$\Rightarrow$3x + 2x – 7 = 8
Clubbing both the terms with x on the left hand side to obtain:-
$\Rightarrow$5x – 7 = 8
Taking 7 from subtraction in the left hand side to addition in right hand side, we will get:-
$\Rightarrow$5x = 7 + 8
Simplifying it finally to obtain:-
$\Rightarrow$x = 3
Therefore, y = 6 – 7 = - 1

Hence the answer is x = 3 and y = - 1.

Note:
The students must note that we also have alternate ways to solve the same.
Alternate way:
We will add the equation number 2 to the equation number 1 to obtain the following:-
$\Rightarrow${2x – y} + {3x + y} = 7 + 8
Now, simplifying the brackets on the left hand side:-
$\Rightarrow$5x = 15
$\Rightarrow$x = 3
Thus putting this in equation 1 gives y = -1.