Question

solve the pair of equation :x + 2y= -1; 2x - 3y = 12​

Answer 1

Solution

we have,

• x + 2y = -1 ......(i)
• 2x - 3y = 12 ........(ii)

from eq.(i) x + 2y = -1

• x = - 1 - 2y .........(iii)

now, substitute the value of x from (iii) in (ii)

$: \bold{ \implies 2( - 1 - 2y) - 3y = 12} \\ \\ : \bold{ \implies - 2 - 4y - 3y = 12 }\: \: \: \: \: \\ \\ \bold{ : \implies - 7y = 12 + 2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies - 7y = 14 }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \bold{ \implies y = \cancel\frac{14}{ - 7} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \boxed{ \bold{\orange{y = - 2}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now, substitute the value of y in (iii)

$\bold { : \implies \: x = - 1 - 2( - 2) } \\ \\ \bold{ : \implies x = - 1 + 4} \: \: \: \: \: \: \: \: \: \\ \\ : \implies \boxed{ \orange { \bold{x = 3}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, value of y is -2 and value of x is 3