Question

solve the following pair of linear equations by elimination and substirution method(8x+5y=9) (3x+2y=4)
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Answer 1

solution-

8x+5y=9 - eq 1

3x+2y=4 - eq 2

eq 1* 2=16x+10y=18

eq 2*5=15x+10y=20

(-) (-) (-)

= x = -2

if x=-2, then y =

3x+2y=4

3×(-2)+2y=4

-6+2y=4

2y=4+6=10

y=10/2=5

x=-2, y=5

Answer 2

$\large\bf\underline {To \: find:-}$

• Value of x and y by substitution and elimination method.

$\large\bf\underline{Given:-}$

Equations :-

• 8x + 5y = 9
• 3x + 2y = 4

$\huge\bf\underline{Solution:-}$

➳ 8x + 5y = 9 .......1)

➳ 3x + 2y = 4 .......2)

☀ By substitution method :-

• ༒ From equation 1)

➥ 8x + 5y = 9

➥ 8x = 9 - 5y

➥ x = (9 -5y)/8....3)

༒Substituting value of x in 2)

➻ 3x + 2y = 4

➻ 3(9-5y)/8 + 2y = 4

➻ (27 - 15y) /8 + 2y = 4

➻ (27 - 15y + 16y)/8 = 4

➻ 27 + y = 32

➻ y = 32 - 27

• y = 5

❈ putting Value of y in eq (3)

➛ x = (9 - 5y )/8

➛ x = (9 - 5 ×5)/8

➛ x = (9 - 25)/8

➛ x = -16/8

• x = -2

So, Value of x and y is 8 and -11 by substitution method.

༒ BY Elimination method :-

❈ Multiplying eq 1) by 2 and eq 2) by 5

⪼ (8x + 5y = 9) × 2

⪼ (3x + 2y = 4) × 5

⠀⠀⠀⠀⠀16x + 10y = 18

⠀⠀⠀⠀⠀15x + 10y = 20

⠀⠀⠀⠀⠀ --⠀⠀ --⠀⠀⠀--⠀⠀

⠀⠀⠀⠀⠀ x ⠀⠀⠀⠀ = - 2

• x = -2

❈ putting value of x in 2)

➻ 3x + 2y = 4

➻ 3 ×(-2) + 2y = 4

➻ -6 + 2y = 4

➻ 2y = 10

➻ y = 10/2

• y = 5

Hence,

• ☀ Value of x = -2
• ☀ Value of y = 5

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