Solve the following systems of equations:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
Answers
Given pair of system of equation :
0.5x + 0.7y = 0.74 …………...( 1 )
0.3x - 0.5y = 0.5 …………...( 2 )
On multiplying eq 1 & 2 both sides by 100 :
50x + 70y = 74 ……….... (3)
30x + 50y = 50 ………... (4)
From eq (3) :
50x = 74 - 70y
x = (74 - 70y)/50 …………(5)
On Substituting the value of x in equation (4) we get :
30x + 50y = 50
30 (74 - 70y)/50 + 50y = 50
3(74 - 70y)/5 + 50y = 50
[(222 - 210y) + 250y]/5 = 50
[222 - 210y + 250y] = 50 × 5
40y = 250 - 222
40y = 28
y = 28/40 = 7/10
y = 0.7
On putting the value of y in the equation (5) :
x = (74 - 70y)/50
x = (74 - 70 × 0.7)/50
x = (74 - 49)/50
x = 25/50
x = 5/10
x = 0.5
Hence, the value of the given system of equation is x = 0.5 and y = 0.7.
Hope this answer will help you…
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Step-by-step explanation:
0.5 x +0.7 y = 0.74 (i)
multiply 10 on both sides in (i)
=> 5x+7y=7.4
0.3 x + 0.5 y =0.5 (ii)
multiply 10 on both sides in (ii)
3 x + 5 y = 5
y=1-0.6x (from ii equation)
Now, Substitute value in equation i
5x+7y = 5x + 7(1-0.6x)=7.4
=>5x +7-4.2x =7.4
=>0.8x+ 7 = 7.4
=>x=0.5
Now substitute x value in any equation.
Let us take the second equation.
0.3x + 0.5y =0.5
(0.3×0.5)+0.5y= 0.5
0.3+y= 1
∴y=0.7
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