Question

Elimination
5x-4y=1 , x-2y = 3​

Answer 1

Answer:

5x-4y=1--------(1)

x-2y=3----------(2)

Multiply eqn (2) with 2 we get

2x-4y=6----------(3)

Subtract eqn (3) from (1) we get

x=7

now putting value of x =7

7-2y=3

-2y=3-7

y = -4/-2

y=2

(x, y) = (7, 2)

Answer 2

Answer: $x = \frac{-5}{3}$ &  $y = \frac{-7}{3}$

Explanation:

Given pair of linear equations:

• 5x - 4y = 1 -----------------------( 1 )
• x - 2y = 3 ------------------------( 2 )

To solve: The pair of linear equations by elimination method

Proof:

Multiplying equation ( 2 ) by  2, we get:

= 2 ( x - 2y = 3 )

⇒ 2x - 4y = 6 --------------------------( 3 )

Now, subtracting equation ( 1 ) from equation ( 3 ), we get:

= 2x - 4y - ( 5x - 4y) = 6-1

⇒ 2x - 4y - 5x + 4y = 5

⇒ 2x - 5x -4y + 4y = 5

⇒ -3x = 5

⇒ $x = \frac{-5}{3}$

Substituting the value of x in equation ( 2 ), we get:

= x - 2y = 3

⇒ $\frac{-5}{3} - 2y = 3$

⇒ $-2y = 3 + \frac{5}{3}$

⇒ $-2y = \frac{9 + 5}{3}$

⇒ $-2y = \frac{14}{3}$

⇒ $y = \frac{-14}{3 X 2 }$

⇒ $y = \frac{-7}{3}$

Hence, $x = \frac{-5}{3}$ &  $y = \frac{-7}{3}$. Proved.

Hope you got that.

Thank You.