Question

Solve the following pair of linear equation by substitution method 2x-3y=19 and 3x-2y=21​

Answer 1

GIVEN :-

• 2x - 3y = 19.
• 3x - 2y = 21.

TO FIND :-

• The value of x and y.

SOLUTION :-

$\\ : \implies \displaystyle \sf \: 2x - 3y = 19 \: \: \: \: \: \: \: \: \: \bigg \lgroup 1\bigg \rgroup$

$: \implies \displaystyle \sf \: 3x - 2y =2 1 \: \: \: \: \: \: \: \: \: \bigg \lgroup 2\bigg \rgroup$

From Equation 1,

$\\ : \implies \displaystyle \sf \: 2x - 3y = 19$

$: \implies \displaystyle \sf \: 2x = 19 + 3y$

$: \implies \underline{ \boxed{ \displaystyle \sf \: x = \frac{19 + 3y}{2} }}$

Substitute the value of x in equation 2,

$\\ : \implies \displaystyle \sf \: 3x - 2y = 21$

$: \implies \displaystyle \sf \: 3 \times \frac{19 + 3y}{2} - 2y = 21$

$: \implies \displaystyle \sf \: \frac{3(19 + 3y)}{2} - 2y = 21$

$: \implies \displaystyle \sf \: \frac{57 + 9y}{2} - 2y = 21$

$: \implies \displaystyle \sf \: \frac{57 + 9y - 4y}{2} = 21$

$: \implies \displaystyle \sf \: \frac{57 + 5y}{2} = 21$

$: \implies \displaystyle \sf \: 57 + 5y = 21 \times 2$

$: \implies \displaystyle \sf \: 57 + 5y = 42$

$: \implies \displaystyle \sf \: 5y = 42 - 57$

$: \implies \displaystyle \sf \: 5y = - 15$

$: \implies \displaystyle \sf \: y = \frac{ - 15}{5}$

$: \implies \underline{ \boxed{\displaystyle \sf \: y = - 3}}$

Substitute the value of y in the equation 1,

$\\ : \implies \displaystyle \sf \: 2x - 3y = 19$

$: \implies \displaystyle \sf \: 2x - 3 \times -3 = 19$

$: \implies \displaystyle \sf \: 2x + 9 = 19$

$: \implies \displaystyle \sf \: 2x = 19 -9$

$: \implies \displaystyle \sf \: 2x = 10$

$: \implies \displaystyle \sf \: x = \frac{10}{2}$

$: \implies \underline{ \boxed{ \displaystyle \sf \: x = 5}}$

Hence the required value of x is 5 and required value of y is -3.

Answer 2

Answer:

Given :

• 2x - 3y = 19 ...... 1

• 3x - 2y = 21 ..... 2

To Find :

• The value of x and y

Solution :

Concept :

• Use a line already drawn on a graph and its demonstrated points before creating a linear equation.

• Follow this formula in making slope-intercept linear equations: y = mx + b. Determine the value of m, which is the slope (rise over run).

Find the slope by finding any two points on a line.

Multiplying (1) by 2 & (2) by 3

4x - 6y = 38 .... 3

9x - 6y = 63 ..... 4

Subtracting (3) from (4)

9x - 6y = 63

- 4x - 6y = 38

(+) (-)

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

5x = 25

x = 5

Putting x = 5 in (1)

2(5) - 3y = 19

10 - 3y = 19

-3y = 19 - 10

-3y = 9

y = -3

(x, y) = (5, -3)

Hence the value of x = 5 and y = 3