Question

8x-3y=12 : 5x-2y=7 elimnatination method

Answer 1

$\sf{ \large{8x - 3y = 12 - - - - (1)}} \\ \\ \sf{ \large{5x - 2y = 7 - - - - (2)}}$

Eliminating by subtracting eq (2) × 3 from eq (1) × 2

$\sf{16x - 6y = 24} \\ \sf{15x - 6y = 21} \\ \underline{ \: ( - ) \: \: \: \: ( + ) \: \: \: ( - ) \: \: \: \: } \\ \: \underline{ \sf{ \: \: x + \: 0 \: \: \: \: = 3 \: \: \: \: \: \: }} \\ \\ \longrightarrow \: \bf{x = 3}$

Putting this value of x in eq (2)

$\longrightarrow \: \sf{5x - 2y = 7} \\ \\ \longrightarrow \: \sf{(5 \times 3) - 2y = 7} \\ \\ \longrightarrow \: \sf{15 - 2y = 7} \\ \\ \longrightarrow \: \sf{ - 2y = 7 - 15} \\ \\ \longrightarrow \: \sf{ - 2y = - 8} \\ \\ \longrightarrow \: \sf{y = \dfrac{ - 8}{ - 2} } \\ \\ \longrightarrow \: \bf{y = 4}$

Answer :

• x = 3
• y = 4

Answer 2

Given:-

8x-3y=12 ________(1)

5x-2y=7 _________(2)

To find:-

The given equations in elimnatination method.

Solution:-

By eliminating eq(2) with 3 from eq(1) with 2, we get,

16x - 6x = 24_______(3)

15x - 6y = 21________(4)

By subtracting eq (3) and eq (4), we get,

$16x - 6y = 24 \\ 15x - 6y = 21 \\ ( - ) \: \: ( + ) \: \: \: \: \: ( - ) \\ - - - - - - - \\ x + \: \: \: \: 0 \: \: \: = \: 3$

⇒ x = 3

Putting the value of x in eq(2), we get,

$⇒5x - 2y = 7 \\ ⇒(5 \times 3) - 2y = 7 \\ ⇒15 - 2y = 7 \\ ⇒ - 2y = 7 - 15 \\ ⇒ - 2y = - 8 \\ ⇒y = \frac{ - 8}{ - 2} \\ ⇒y = 4$

Final result:-

Hence the value of x and y is 3 and 4.

● x = 3

● y = 4.