Question

if a+ b= 13 and a -b= - 6 find a and b

Answer 1

Answer:

a=7/2 b=19/2

Step-by-step explanation:

a+b=13

a-b=-6

2a=7

a=7/2

a+b=13

b=13-7/2

b=19/2

Answer 2

Step-by-step explanation:

$a + b = 13 \\ \\ a - b = - 6 \\ \leadsto \bold{a = b - 6} \\ \\ Substituting \: \bold{a = b - 6} \: on \: \bold{ a + b = 13} \\ \bold{b - 6} + b = 13 \\ 2b = 13 + 6 \\ 2b = 19 \\ b = \frac{19}{2} \\ \fbox \bold{b= 9.5} \\ \\ Substituting \: \bold{b = 9.5} \: on \: \bold{a = b - 6} \\ a = \bold{9.5} - 6 \\ \fbox \bold{ a = 3.5}$

$\bold{Checking - } \\ \\ Substituting \: the \: value \: of \: \bold{a}\: and \: \bold{b} \: \\ on \: \bold{both \: equations} \: for \: \bold{checking} \: \\ that \: our \: answer \: is \: correct \: or \: not \\ \\ a + b = 13 \\ \bold{3.5 + 9.5 = 13} \\ 13 = 13 \\ LHS \: = RHS \\ And \\ a - b = - 6 \\ \bold{3.5 - 9.5 = - 6} \\ - 6 = - 6 \\ LHS = RHS \\ \\ Hence, \\ Proved \: that \: our \: Answer \: is \: Absolutely \: Correct$