Question

Solve the following systems of equations:
$
  0.4x + 0.3y = 1.7 \\
  0.7x - 0.2y = 0.8 \\
$

Answer 1

Hint – Multiply the first equation by 7 and the second equation by 4, then add or subtract these equations to find the value of x and y.

Complete step-by-step answer:
We have been given the equations-
$
  0.4x + 0.3y = 1.7 - (1) \\
  0.7x - 0.2y = 0.8 - (2) \\
$
Now multiplying the equation (1) by 7 and equation (2) by 4, we get-
$
  2.8x + 2.1y = 11.9 - (3) \\
  2.8x - 0.8y = 3.2 - (4) \\
$
Subtract equation (4) from equation (3), we get-
$
  2.8x + 2.1y - (2.8x - 0.8y) = 11.9 - 3.2 \\
  2.9y = 8.7 \\
  y = 3 \\
 $
Putting the value of y in equation (1), we get-
$
  0.4x + 0.3 \times 3 = 1.7 \\
  0.4x + 0.9 = 1.7 \\
  0.4x = 1.7 - 0.9 \\
  0.4x = 0.8 \\
  x = 2 \\
 $
Hence, the values of x and y are 2, 3 respectively.

Note- Whenever such types of questions appear then always write the equations given in the question 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.