Question

Solve the following pair of equations:
3 – (x – 5) = y + 2, 2(x + y) = 4 – 3y.
$
  {\text{A}}{\text{. x = }}\dfrac{7}{2},{\text{y = }}\dfrac{{ - 9}}{5} \\
  {\text{B}}{\text{. x = }}\dfrac{1}{6},{\text{y = }}\dfrac{{ - 4}}{3} \\
  {\text{C}}{\text{. x = }}\dfrac{{26}}{3},{\text{y = }}\dfrac{{ - 8}}{3} \\
  {\text{D}}{\text{. x = }}\dfrac{6}{5},{\text{y = }}\dfrac{{ - 7}}{3} \\
$

Answer 1

Hint – Transform one equation such that the variable x is in terms of y. Substitute y in the other equation. Now, obtain the value of y and substitute it in the previous equation for x.

Complete step by step answer:
Given, 3 – (x – 5) = y +2
⟹3 – x + 5 = y + 2
⟹8 – x = y + 2
⟹x = 6 – y ---- Equation 1
Now substitute x in 2(x+ y) = 4 – 3y
⟹2 (6 – y + y) = 4 – 3y
⟹12 = 4 – 3y
⟹3y = - 8
⟹y = $\dfrac{{ - 8}}{3}$
We obtained the value of y, substitute it Equation 1 to find the value of x
$
   \Rightarrow {\text{x = 6 - }}\left( {\dfrac{{ - 8}}{3}} \right) \\
   \Rightarrow {\text{x = }}\dfrac{{26}}{3} \\
  {\text{Therefore x = }}\dfrac{{26}}{3}{\text{ and y = }}\dfrac{{ - 8}}{3} \\
$
Hence Option C is the correct answer.

Note – It is evident that this is a problem which is a clear case of 2 equations and 2 variables. Upon solving we obtain the values of both the variables. The key is to transform one of the equations such that we have one variable in terms of another. Then the other equation reduces into a single variable equation and becomes easier to solve. On finding the value of one variable the other can be found simply by substituting the value found.