Question

7(y + 3) - 2(x + 2) = 14
4(y-2) + 3(x - 3) = 2 solve using substitution method​

Answer 1

Given equation

7(y + 3) - 2(x + 2) = 14                  (i)

4(y - 2) + 3(x - 3) = 2                     (ii)

To find

Value of x and y by using Substitution method

Now take both equation and simplify into simplest form  

7(y + 3) - 2(x + 2) = 14                  (i)

7y + 21 - 2x + 4 = 14

7y - 2x + 25 = 14

7y - 2x = 14 - 25

7y - 2x = -11

2x - 7y = 11         (iii)

Similarly

4(y - 2) + 3(x - 3) = 2                     (ii)

4y - 8 + 3x - 9 = 2

3x + 4y - 17 = 2

3x + 4y = 17 + 2

3x + 4y = 19              (iv)

we get

2x - 7y = 11         (iii)

3x + 4y = 19              (iv)

Now using substitution method so take (iii)

2x - 7y = 11            (iii)

2x = 11 + 7y

x = (11 + 7y)/2         (v)

put the value of x on (iv) eq

3x + 4y = 19              (iv)

3(11 + 7y)/2 + 4y = 19

by taking lcm we get

3(11 + 7y) + 8y = 19×2

33 + 21y + 8y = 38

33 + 29y = 38

29y = 38 - 33

29y = 5

y = 5/29

now put the value of y on (v) eq

x = (11 + 7y)/2         (v)

x =( 11 + 7×5/29)/2

x = ( 11 + 35/29)/2

x = {( 319 + 35)/29}/2

x = 354/29 × 1/2

x =  177/29

Answer

x = 177/29  and y = 5/29

Answer 2

• x=5 and y =1

Step-by-step explanation:

Given :7 (y+3)-2 (x+2)=147(y+3)−2(x+2)=14 --A

• 4 (y-2)+3 (x-3)=24(y−2)+3(x−3)=2 --B

To Find: Solve by substitution method

Solution:

Simplify A

$\sf ⟹ 7 (y+3)-2 (x+2)=147(y+3)−2(x+2)=14$

$\sf⟹ 7y+21-2x-4=147y+21−2x−4=14$

$\sf⟹ 7y-2x+17=147y−2x+17=14$

$\sf ⟹ 7y-2x=-37y−2x=−3$

$\sf⟹ 2x-7y=32x−7y=3 ---1$

Simplify B

$\sf⟹ 4 (y-2)+3 (x-3)=24(y−2)+3(x−3)=2$

$\sf ⟹ 4y-8+3x-9=24y−8+3x−9=2$

$\sf ⟹ 4y+3x-17=24y+3x−17=2$

$\sf ⟹ 4y+3x=194y+3x=19 ---2$

Substitute the value of x from 1 in 2

$\sf⟹ 4y+3(\frac{3+7y}{2})=194y+3(23+7y )=19$

$\sf ⟹ 8y+9+21y=388y+9+21y=38$

$\sf ⟹ 29y=2929y=29$

$\sf ⟹ y=1y=1$

Substitute the value of y in 2

$\sf ⟹ 4y+3x=194y+3x=19$

$\sf ⟹ 4(1)+3x=194(1)+3x=19$

$\sf ⟹ 3x=153x=15$

$\sf →x=5x=5$

✵Hence x = 5 and y =1✵

@AbhinavRocks10