Question

the solution of linear pairs of equations 5x+2y=16 and7x-4y=2

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

Given equations :-

1. 5x + 2y = 16
2. 7x - 4y = 2

Solution :-

Multiply throughout equation 1 by 2,

2 × 5x + 2 × 2y = 2 × 16

10x + 4y = 32 -----> 3

Solve equations 2 and 3 simultaneously by elimination method.

Add equation 3 to 2,

10x + 4y = 32

7x - 4y = 2

----------------

17x = 34

x =$\bf\large\frac{34}{17}$

$\bf{\large{\underline{\boxed{\rm{\green{x =\: 2}}}}}}$

Substitute x = 2 in equation 1,

5x + 2y = 16 ---->1

5 (2) + 2y = 16

10 + 2y = 16

2y = 16 - 10

2y = 6

y =$\bf\large\frac{6}{2}$

$\bf{\large{\underline{\boxed{\rm{\pink{y\:=\:3}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\blue{Solution :\:(x, y) =(2,3)}}}}}}$

$\bf{\huge{\underline{\boxed{\mathfrak{\purple{Verification:}}}}}}$

For equations 1:-

• 5x + 2y = 16

Plug the values of x and y in the equation,

5 (2) + 2(3) = 16

10 + 6 = 16

16 = 16

LHS = RHS.

First equation is verified.

For second equation :-

• 7x - 4y = 2

Repeat the same procedure, plug the values of x and y in the above equation.

7 ( 2) - 4( 3) = 2

14 - 12 = 2

2 = 2

LHS = RHS.

Both the answers are right as per the verification!

Answer 2

$\red {\huge {\underline{ \frak{Your \: answEr : }}}} \:$

$\green {\large{ \underline{\mathcal{\star \:Given : }}}}$

• Linear Pairs of two Variables

5x + 2y = 16 and, 7x - 4y = 2

$\green{\large{ \underline{\mathcal{\star \: To \: Find : }}}}$

• Solution of Liner Pair of two Variables Given in Question.

$\green{\large{ \underline{\mathcal{\star \: Solution : }}}}$

$\implies \tt{5x + 2y = 16 }$ (¡)

$\implies \tt{7x - 4y = 2}$ (¡¡)

Multiplying (¡) by 2

$\implies \tt{10x + 4y = 32}$

$\implies \tt{7x - 4y = 2}$

______________________________

$\implies \tt{17x = 34}$

$\huge\purple{\boxed{ \implies \tt{ x = 2 }}}$

$\blacksquare$ Putting the Value of x in (¡¡) Equation

$\implies \tt{7x - 4y = 2}$

$\implies \tt{7 \times 2 - 4y = 2}$

$\implies \tt{14 - 2 = 4y}$

$\implies \tt{4y = 12}$

$\huge\purple{\boxed{ \implies \tt{ y = 3 }}}$

$\odot$ Solutions of this Linear Equation is :

$\huge ✓~~\bold{x = 2} \\ \\ \huge ✓~~ \bold{y = 3}$