7x+3y=8
6 −3 =5
For the solution (x, y) to the system of equations above, what is the value of x − y ?

Options

A. `-4/3`
B. `2/3`
C. `4/3`
D. `22/3`

Answer

B

Explanation

Adding the equations side-by-side eliminates y, as shown below.
`{:(7x+3y=8),(6x-3y=5),(overline(13x+0=13)):}`
Solving the obtained equation for x gives x = 1. Substituting 1 for x in the first equation gives
7(1) + 3y = 8. Subtracting 7 from both sides of the equation yields 3y = 1, so `y =1/3`. Therefore , the value of x-y is `1-1/3` , or `2/3`.
Choice C is incorrect because `1+1/3=4/3`
is the value of x + y, not x − y. Choices A and D are
incorrect and may be the result of some computational errors.