Question

Solve the following given equations in x and y:-



1)3x+2y=11


2x+3y=4





2) 8x+5y=9

3x+2y=4

3) 217x+131y=913


131x+217y=827

Answer 1

Answer:

1)3x +2y =11==1eq

2x + 3y =4 ===2eq

By elimination method :-

(3x +2y=11) ×2

(2x+3y=4)×3

6x +6y=22

6x+9y=12

- - -

========

-3y = 10

========

y =-10/3

.

put y in 1 st eq

=》3x +2(-10/3)=11

=》9x -20=33

=》9x=33+20

=》9x=50

x=50/9

▪X=50/9 and y =-10/3 ans

2)8x+5y=9 ===1eq

3x+2y=4====2eq

By elimination method

(8x+5y=9 )×3

(3x+2y=4)×8

24x+15y=27

24x+16y=32

_ _ _

==========

-y= -5 , y =5

==========

put y in 1 st equation

8x+5(5)=9

=》8x +25=9

=》8x=9 -25

=》8x=-16

=》x=-2

▪y=5 and x =-2 ans

3)217x+131y=913===1 eq

131x+217y=827=====2eq

By elimination method

(217x+131y=913)×131

(131x+217y=827)×217

=》28427x+17161 y= 119603

28427 x +47089y =179459

_ _ _

===========================

-29928 y = -59856

y = 59856/29928

Y =2

put value of y in eq 1

=》217x+131(2)=913

=》 217x + 262 =913

=》217x=913 -262

=》217x=651

=》x=651/217

=》x=3

▪x=3 and y = 2 answer

Answer 2

Solution:

$\mathfrak { \boxed{\purple {{\star}}{\bold{ \bold{ \mathfrak \red{ \underline { \underline{ \underline {{{First \: Question}}}}}}}}}}}$

3x+2y= 11 -(1)

2x+3y=4 -(2)

By eliminating y from the above equations. The coefficients of y in the given equations are 2 and 3 respectively. The L.C.M of 2 and 3 is 6. So,we need to make the coefficients equal to 6 in both the equations.

Multiplying equation -(1)by 3 and equation -(2) by 2, we get:

9x+6y=33 -(3)

4x+6y=8 -(4)

Subtracting -(4) from -(3),we get:

5x= 25

⟹x=5

Substituting $\bold{x=5}$in equation -(1),we get:

15+2y= 11

⟹2y= -4

⟹y= -2

$\red \star\boxed{ \bold{ \orange{\mathfrak{ \underline{ \underline{x = 5}}}}}}$

$\blue \star\boxed{ \bold{ \pink{\mathfrak{ \underline{ \underline{y = - 2}}}}}}$

$\mathfrak { \boxed{\pink {{\star}}{\bold{ \bold{ \mathfrak \orange{ \underline { \underline{ \underline {{{Second \: Question}}}}}}}}}}}$

8x+5y= 9 -(1)

3x+2y= 4 -(2)

Let's eliminate x from the given equations. The coefficients of x in the given equations are 8 and 3 respectively. The L.CM of 8 and 3 is 24. So, we need to make the coefficients equal to 24.

Multiplying both sides of equation -(1)by 3 and equation -(2) by 8, we get:

24x+15y= 27 -(3)

24x+ 16y= 32 -(4)

Subtracting -(4)from -(3), we get:

-y= -5

⟹ y= -5

Putting y=5 in -(1),we get:

8x+25= 9

8x= -16

x= -2

$\red \star\boxed{ \bold{ \pink{\mathfrak{ \underline{ \underline{ x= - 2}}}}}}$

$\red \star\boxed{ \bold{ \orange{\mathfrak{ \underline{ \underline{ y= 5}}}}}}$

$\mathfrak { \boxed{\purple {{\star}}{\bold{ \bold{ \mathfrak \pink{ \underline { \underline{ \underline {{{Third\: Question}}}}}}}}}}}$

217x+131y= 913 -(1)

131x+217y= 827 -(2)

Adding equations -(1)and -(2),we get:

348x+348y= 1740

⟹ x+y= 5 -(3)

Subtracting equation -(2) from -(1),we get:

86x-86y= 86

86x-86y= 86⟹x-y= 1 -(4)

Adding equation -(3) and -(4),we get:

2x= 6

⟹x= 3

Putting x= 3, in equation -(3), we get y= 2

$\red \star\boxed{ \bold{ \orange{\mathfrak{ \underline{ \underline{ x= 3}}}}}}$

$\:\red \star\boxed{ \bold{ \pink{\mathfrak{ \underline{ \underline{ y= 2}}}}}}$