Question

$2u + 3v = 13 \\ 5u - 4v = - 2$
​

Answer 1

Step-by-step explanation:

(2u +3v =13 )5

(5u - 4v =-2)2

10u + 15v = 65

10u - 8v = -4

Subtract

23v=69

v=3

so u=2

Answer 2

$\large \bold{ \underline{ \underline{ \: Answer : \: \: \: }}}$

$\to$ v = 3

$\to$ u = 7/2

$\large \bold{ \underline{ \underline{ \: Explaination : \: \: \: }}}$

Given ,

$\to$ 2u + 3v = 13 ----- eq(i)

$\to$ 5u - 4v = -2 ----- eq (ii)

Multiply eq (i) by 5 and eq (ii) by 2 we get ,

$\to$ 10u + 15v = 65 ------- eq (iii)

$\to$ 10u - 8v = - 4 -------- eq (iv)

Subtract eq (iv) from eq (iii) ,

$\to$ 10u + 15v - (10u - 8v) = 65 - (-4)

$\to$ 15v + 8v = 65 + 4

$\to$ 23v = 69

$\to$ v = 69/23

$\to$ v = 3

Put the value of v = 3 in eq (i) ,

$\to$ 2u + 3 × 2 = 13

$\to$ 2u + 6 = 13

$\to$ 2u = 13 - 6

$\to$ 2u = 7

$\to$ u = 7/2

Hence , v = 3 and u = 7/2