Question

How do you solve this system of equations:
 $ - 0.8x + 0.6y = 2 $ and $ 3.2x - 0.4y = 4? $

Answer 1

Hint: Here we are given two sets of equations, first of all we will convert the coefficient of any of the variables common in both the set of equations. Then will use the elimination method to get the values of x and y.

Complete step-by-step answer:
Take the given expressions: $ - 0.8x + 0.6y = 2 $ and
 $ 3.2x - 0.4y = 4 $
Multiply both the given equations with the number
 $ - 8x + 6y = 20 $ …. (A)
 $ 32x - 4y = 40 $ ….. (B)
Take out common multiples from both the sides of the equation in (B)
 $ 4(8x - y) = 4(10) $
Common factors from both the sides of the equation cancels each other.
 $ 8x - y = 10 $ ….. (C)
Add equations (A) and (B)
Add the left hand side of both the equations and the right hand side of the equations.
 $ - 8x + 6y + 8x - y = 20 + 10 $
Like values with the same value and opposite sign cancels each other.
\[ \Rightarrow 6y - y = 30\]
Simplify the above expression-
\[ \Rightarrow 5y = 30\]
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
\[ \Rightarrow y = \dfrac{{30}}{5}\]
Common factors from the numerator and the denominator cancel each other.
\[ \Rightarrow y = 6\]
Place above value in equation (C)
 $ 8x - 6 = 10 $
Make the “x” subject, when you move any term from one side of the equation to the opposite side then the sign of the terms also changes.
 $
  8x = 10 + 6 \\
  8x = 16 \\
  x = \dfrac{{16}}{8} \\
  x = 2 \;
  $
Hence, the required values are –
 $ (x,y) = (2,6) $
So, the correct answer is “(2,6)”.

Note: Always remember that when we expand the brackets or open the brackets, the sign outside the bracket is most important. If there is a positive sign outside the bracket then the values inside the bracket does not change and if there is a negative sign outside the bracket then all the terms inside the bracket changes. Positive terms change to negative and negative term changes to positive. While doing simplification remember the golden rules-
I.Addition of two positive terms gives the positive term
II.Addition of one negative and positive term, you have to do subtraction and give signs of bigger numbers whether positive or negative.
III.Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.