0.5x+0.8y=0.44,0.8x+0.6y=0.5
Answers
First we have to make the given equations in the form of a₁ x + b₁ y + c₁ = 0,a₂ x + b₂ y + c₂ = 0.
0.5 x + 0.8 y = 0.44 ----- (1)
0.8 x + 0.6 y = 0.5 ----- (2)
To make the decimal numbers into integers we have to multiply the first equation by 100 and the second equation by 10.
50 x + 80 y - 44 = 0 ----- (1)
8 x + 6 y - 5 = 0 ----- (2)
x/(-400-(-264)) = y/(-352 -(-250)) = 1/(300-640)
x/(-400+264) = y/(-352+250)) = 1/(-340)
x/(-136) = y/(-102) = 1/(-340)
x/(-136) = 1/(-340) y/(-102) = 1/(-340)
x = (-136)/(-340) y = (-102)/(-340)
x = 0.4 y = 0.3
Therefore solution is (0.4,0.3).
Verification:
Now let us apply the answer that we got in the first or second equation to check whether we got correct answer or not.
0.8 x + 0.6 y = 0.5
0.8(0.4) + 0.6(0.3) = 0.5
0.32 + 0.18 = 0.5
0.5 = 0.5
0.8x+0.6y=0.5..........¡¡×5
4x+6.4y=3.52
4x+3y=2.5
6.1y=1.02
=>y=1.02/6.1
=>y=0.17
Putting y=0.17 in 1
0.5x+0.8y=0.44
=>0.5x=0.304
=>x=0.608