Question

Solve the following system of equations by elimination method
2x+3y = 4,3x-y=-5​

Answer 1

Answer:

Step-by-step explanation:

2x+3y=4

3x*3-3*y=-5*3

2x+3y=4

9x-3y=-15

11x=-11

X=-11/11

X=-1

Put the value of x in eq.no 1

2x+3y=4

2*-1+3y=4

-2+3y=4

3y=4+2

3y=6

Y=6/3

Y =2

Answer 2

$\Large\underline\mathbb\blue{ANSWER}$

$\tt{ 2x + 3y = 4...(i)} \\ \tt{3x - y = - 5 ...(ii)}$

After making coefficient of y equal,

$\tt{2x + 3y = 4...(iii)}\\ and \\ \tt{9x - 3y = - 45 ...(iv)}$

Subtracting equation (iv) from equation (iii),

$\: \: \: \: \: \: \: \: \: \: \tt{(9x + 3y) - (2x + 3y) = - 45 - 4} \\ \\ \implies \tt{2x + \cancel{3y} - 9x - \cancel{ 3y} = 49} \\ \\ \implies \tt{ - 7x = - 49} \\ \\ \implies \tt{x = \frac{ \cancel{-} 49}{ \cancel{-} 7} } \\ \\ \implies \boxed{ \tt{ \pink{x = 7}}}$

Substituting the values in equation (i),

$\: \: \: \: \: \: \: \: \: \: \: \tt{2x + 3y = 4} \\ \\ \implies \tt{2( - 7)} + 3y = 4 \\ \\ \implies \tt{ - 14 + 3y = 4} \\ \\ \implies \tt{3y = - 18} \\ \\ \implies\tt{y = \frac{ - 18}{3} } \\ \\ \implies \boxed{ \pink{ \tt{y = - 6}}}$

hope it's helpful ✅✅✅