Question

3 2 6
2. Solve 2 - 3 = 1 and 2x - 4y = - 24 and hence find the value of 'm' for which
= mx-3​

Answer 1

Correct Question :

Solve 2x -3y = 1 and 2x -4y = -24 and hence Find the value of m for which 0 = mx -3.

Solution :

We have equation,

$\tt \dagger \: \: \: \: \: 2x - 3y = 1. \: \: \: \: \: - (1)$

$\tt \dagger \: \: \: \: \: 2x - 4y = - 24. \: \: \: \: \: - (2)$

Let try to solve my Substitution method Apply

Taking equation ( 2 )

$\tt\longmapsto 2x - 4y = - 24$

$\tt\longmapsto x - 2y = - 12.$

$\tt \longmapsto x = 2y - 12. \: \: \: \: \: - (3)$

Putting the value of x in Equation ( 1 ) We get,

$\tt\longmapsto 2x - 3y = 1.$

$\tt\longmapsto 2(2y - 12) - 3y = 1.$

$\tt \longmapsto 4y - 24 - 3y = 1.$

$\tt \longmapsto y = 25.$

Now, Putting the value of y in Equation ( 3 )

$\tt \longmapsto x = 2y - 12.$

$\tt\longmapsto x = 2(25) - 12$

$\tt \longmapsto x = 50 - 12.$

$\tt\longmapsto x = 38.$

$\rule{90}1$

A/Q,

$\tt\dagger \: \: \: \: \: 0= mx - 3$

$\tt \longmapsto 0 = m(38) - 3.$

$\tt \longmapsto 38m = 3.$

$\tt \longmapsto m = \frac{3}{38}$

Therefore, the value of m be 3/ 38

$\rule{200}3$

Verification :

Taking Equation 1.

$\tt\longmapsto 2x - 3y = 1.$

Where as,

• X = 38.
• Y = 25.

$\tt\longmapsto 2( 38 ) - 3( 25 )= 1.$

$\tt\longmapsto 76 - 75= 1.$

$\tt\longmapsto 1 = 1.$

Hance LHS = RHS.

$\rule{90}1$

Taking Equation ( 2 )

$\tt \longmapsto 2x - 4y = - 24.$

$\tt \longmapsto 2( 38 )- 4( 25 )= - 24.$

$\tt \longmapsto 76 - 100 = - 24.$

$\tt \longmapsto -24 = - 24.$

Hance LHS = RHS.