Question

Solve the following systems of equations:
$
  7(y + 3) + 2(x + 2) = 14 \\
  4(y - 2) + 3(x - 3) = 2 \\
$

Answer 1

Hint – We can write the first equation as $2x + 7y = - 11$ and the second equation as $3x + 4y = 19$ after simplification. Now solve these equations.

Complete step-by-step answer:
We have the equations-
$
  7(y + 3) + 2(x + 2) = 14 - (1) \\
  4(y - 2) + 3(x - 3) = 2 - (2) \\
$
Now simplifying the equation (1)-
$
  7(y + 3) + 2(x + 2) = 14 \\
  7y + 21 + 2x + 4 = 14 \\
  2x + 7y = - 11 - (3) \\
 $
Similarly, simplifying equation (2)-
$
  4(y - 2) + 3(x - 3) = 2 \\
  4y - 8 + 3x - 9 = 2 \\
  3x + 4y = 19 - (4) \\
 $
Now, multiplying by 3 in equation (3) and multiplying by 2 in equation (4), we get-
$
  6x + 21y = - 33 - (5) \\
  6x + 8y = 38 - (6) \\
$
Subtracting equation 5 from 6, we get-
$
  6x + 8y - 6x - 21y = 38 + 33 \\
   - 13y = 71 \\
  y = - 5.46 \\
 $
Now putting the value of y in equation (5), we get-
$
  6x + 21( - 5.461) = - 33 \\
  6x - 114.807 = - 33 \\
  6x = 81.807 \\
  x = 13.63 \\
$
Hence, the values of x and y are 13.63 and -5.461 respectively.

Note - Note - Whenever such types of questions appear then always write the equations given in the question and then simplify them to the simplest form. Then by adding and subtracting try to find the value of x or y and then by using the value of either x or y, find the other unknown variable.