Question

0.3x +0.5y = 0.5,
0.5x +0.7y = 0.74
Find the value of x & y by the substitution method​

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Answer 1

Step-by-step explanation:

Given Equations are:

0.3x + 0.5y = 0.5   ------ (i)

0.5x + 0.7y = 0.74  ------ (ii)

Substitution Method:

Multiply (i) & (ii) by 100, we get

30x + 50y = 50    ---- (iii)

50x + 70y = 74     ---- (iv)

Equation (iii) can be written as,

⇒ 30x + 50y = 50

⇒ 30x = (50 - 50y)

⇒ x = (50 - 50y)/30

Substitute x in (iv), we get

⇒ 50(50 - 50y/30) + 70y = 74

⇒ 50(50 - 50y) + 2100y = 2220

⇒ 2500 - 2500y + 2100y = 2220

⇒ -400y = -280

⇒ 40y = 28

⇒ y = 28/40

⇒ y = 0.7

Substitute y = 0.7 in (iii), we get

⇒ 30x + 50y = 50

⇒ 30x + 50(0.7) = 50

⇒ 30x + 35 = 50

⇒ 30x = 15

⇒ x = 0.5

∴ The values of x & y are 0.5 and 0.7

Hope it helps!

Answer 2

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