Question

solve for x and y :
11x + 15y + 23 = 0; 7x - 2y - 20 = 0.
2x+y=7; 4x - 3y+1=0.
23x - 29 y=98; 29x - 23y = 110.
2x+5y=8/3;3x-2y=5/6
4x - 3y=8; 6x-y=29/3
thanks a lot ​

Answer 1

$\boxed{\textbf{\large{Step by step explanation }}}$

◾Solving the given equations by elimination method

◾Here we can eliminate the terms by subtracting or adding of equations both of them ,then we can get the values of x and y

Q1)

➡

11x + 15y + 23 = 0 ;

7x - 2y - 20 = 0

11x + 15y = -23 .....(1)

7x - 2y = 20 ........(2)

◾multiply equation (1) by 7 and multiply equation (2) by 11

7 ( 11x + 15y) = (7)( -23)

77x + 105y = -161 ..........(3)

Now,

11( 7x - 2y) = 20(11)

77x - 22y = 220 ..........(4)

◾subtract equation (4) from (3)

77x + 105y = -161

77x - 22y = 220

(-)......(+)..........(-)

___________________

127y = -381

y =- 3

◾put the value of y in equation (1)

11x + 15(-3)= -23

11x = -23 + 45

11x = 22

x = 2

_________________________________

Q2)

➡

2x + y = 7 ; 4x - 3y +1 = 0

2x + y = 7 .......(1)

4x - 3y = -1........(2)

◾multiply equation (1) by 4 and equation (2) by 2

4(2x + y )= 7 (4)

8x + 4y = 28 ..........(3)

Now,

2(4x - 3y )= -1(2)

8x - 6y = -2 .........(4)

◾subtract equation (4) from (3)

8x + 4y = 28

8x - 6y = -2

(-)...(+)....(+)

_____________

( 10y) = 30)

y = 3

◾put this value of y in equation (1)

2x + y = 7

2x + (3) = 7

2x = 7- 3

x = 4/2

x = 2

__________________________________

Q(3)]

➡

23x - 29y = 98

29x - 23y = 110

23x - 29y = 98 ..........(1)

29x - 23y = 110 ........(2)

◾multiply equation (1) by 29 and equation (2) by 23

(29)(23x - 29y) = 98(29)

667x - 841y = 2842 .......(3)

Now,

(23)(29x - 23y) = 110(23)

667x - 529y = 2530.......(4)

◾subtract equation (4) from (3)

667x - 841y = 2842

667x - 529y = 2530

(-).......(+)........(-)

_____________________

-312 y = 312

y = -1

◾ put this value of y in equation (1)

23x - 29(-1) = 98

23x +29 = 98

23x = 98 - 29

x = 69/23

x = 3

________________________________

Q4)

➡

2x + 5y = 8/3

3x - 2y = 5/6

2x + 5y = 8/3 ........(1)

3x - 2y = 5/6 .........(2)

multiply equation (1) by 3 And

multiply equation (2) by 2

(3)(2x + 5y) =( 8/3) (3)

6x + 15y = 8 ...........(3)

2(3x - 2y) =( 5/6)2

6x - 4y = 5/3 ............(4)

subtract equation (4) from (3)

6x + 15y = 8

6x - 4y = 5/3

(-).....(+)......(-)

______________

19y = 19/3

y =( 19/3)(1/19)

y = 1/3

◾put this value of y in equation (1)

2x + 5(1/3) = 8/3

2x = (8/3) - (5/3)

2x = 3 / 3

x = 1 / 2

________________________________

Q5)

➡

4x - 3y=8

6x-y=29/3

4x - 3y =8 ...........(1)

6x - y =29/3 .....(2)

◾multiply equation (1) by 6 and

multiply equation (2) by 4

(6)(4x - 3y) =8(6)

24x - 18y = 48 ..........(3)

Now,

6x - y =29/3

4(6x - y) = (29/3)(4)

24x - 4y = 116 / 3 ............(4)

◾Subtract equation (4) from (3)

24x - 18y = 48

24x - 4y = 116/3

(-)......(+).......(-)

___________________

- 14y = 48 - ( 116 /3 )

-14y = (144 - 116)/3

-14y =( 28/3 )(1/(-14))

y = - 2 / 3

◾put this value of y in equation (1)

4x - 3( - 2 / 3 )= 8

4x +( 2 ) = 8

4x = 8 - ( 2 )

4x =( 6 )

4x = (6) / 4

x = 3 / 2

________________________________

Answer 2

Happy Birthday to saesae