Question

2x=5y-9 x=2y+8
Solve using substitution method

Answer 1

Answer:

x = 2y + 8 equation no: 01

2x =5y -9 equation no: 02

sunstitute the equation no 1 into equation no 2

2 (2y + 8) = 5y - 9

4y + 16 = 5y - 9

5y - 4y = 16 + 9

y = 25

y = 25 equation no 3

put equation no 1 into equation no 3

x = 2y + 8

x = 2 (25) + 8

x = 50 + 8

x = 58

So,

x = 58 and y = 25

Answer 2

$\large\underline{\sf{Solution-}}$

Given pair of linear equation are

$\rm :\longmapsto\:2x = 5y - 9 - - - - (1)$

and

$\rm :\longmapsto\:x = 2y + 8 - - - - - (2)$

Substitution the value of x from equation (2) from equation (1), is

$\rm :\longmapsto\:2(2y + 8) = 5y - 9$

$\rm :\longmapsto\:4y + 16 = 5y - 9$

$\rm :\longmapsto\:4y - 5y = - 9 - 16$

$\rm :\longmapsto\: - y = - 25$

$\rm\implies \:y = 25$

On substituting the value of y in equation (2), we get

$\rm :\longmapsto\:x = 2 \times 25 + 8$

$\rm :\longmapsto\:x = 50 + 8$

$\rm\implies \:x = 58$

Verification

Consider equation (1)

$\rm :\longmapsto\:2x = 5y - 9$

On substituting the value of x and y, we get

$\rm :\longmapsto\:2 \times 58= 5 \times 25- 9$

$\rm :\longmapsto\:116 = 125 - 9$

$\rm :\longmapsto\:116 = 116$

Hence, Verified

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Basic Concept Used :-

To solve systems using Method of Substitution, follow this procedure:

Select one equation and solve it to get one variable in terms of second variables.

In the second equation, substitute the value of variable evaluated in Step 1 to reduce the equation to one variable.

Solve the new equation to get the value of this variable.

Substitute the value found in to any one of two equations involving both variables and solve for the other variable.