Step 1:
- 0.8x + 0.6y = 2 Let this be equation (1)
3.2x - 0.4y = 4 Let this be equation (2)
Step 2:
To eliminate one variable , say x , we make the coefficient of that variable same in both equations by multiplying the equation by some constant.
here , we will multiply equation (1) by 4 to get
(1) x 4 gives ------- -3.2 x + 2.4 y = 8
Step 3: now the set of equation is
-3.2 x + 2.4 y = 8 and
3.2 x - 0.4 y = 4
Step 4:
we observe that the coefficients of x in both equations are equal but of opposite sign. So we add these two equations in order to eliminate x
Adding the new set of equations we, have:
(-3.2 x + 2.4 y) + (3.2 x - 0.4 y) = 8 + 4
-3.2 x + 2.4 y + 3.2 x - 0.4 y = 12 ---- open brackets
-3.2 x + 3.2 x + 2.4 y - 0.4 y = 12 ---- grouping terms with same variables
0 x + 2.0 y =12
2 y = 12
y = 6
We get the value of y =6
Step 5:
Substitute this value of y in any one of the given equations to find value of x
Substituting y =6 in equation (2):
3.2x - 0.4y = 4
3.2 x - 0.4 x 6 = 4
3.2 x -2.4 = 4
3.2 x = 4 + 2.4 ---- transposition
3.2 x = 6.4
x = 2
Therefore we have x = 2 and y = 6
Step 6: Cross check by substituting values of x and y in any one equation.
Substituting in equation (1), we have
- 0.8x + 0.6y = 2
Left-hand-side of equation is
- 0.8x + 0.6y
- 0.8 x 2 + 0.6 x 6
-1.6 + 3.6
=2 = Right- hand- side of equation.
Hence the obtained values are correct.
