Question

2a-3b =5 , a-2b=4 solve by simultaneous equa​

Answer 1

Correct Question

2a - 3b = 5

a - 2b = 4

Solve the simultaneous equations.

Answer

$\sf \dashrightarrow 2a - 3b = 5 \: \: --- (i)$

$\sf \dashrightarrow a - 2b = 4 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 2a - 3b = 5$

$\sf \dashrightarrow 2a = 5 + 3b$

$\sf \dashrightarrow a = \dfrac{5 + 3b}{2}$

Now, let's find the value of b by second equation.

$\sf \dashrightarrow a - 2b = 4$

$\sf \dashrightarrow \dfrac{5 + 3b}{2} - 2b = 4$

$\sf \dashrightarrow \dfrac{5 + 3b - 4b}{2} = 4$

$\sf \dashrightarrow \dfrac{5 - 1b}{2} = 4$

$\sf \dashrightarrow 5 - 1b = 4 \times 2$

$\sf \dashrightarrow 5 - 1b = 8$

$\sf \dashrightarrow -1b = 8 - 5$

$\sf \dashrightarrow -1b = 3$

$\sf \dashrightarrow b = -3$

Now, let's find the value of a by first equation.

$\sf \dashrightarrow 2a - 3b = 5$

$\sf \dashrightarrow 2a - 3(-3) = 5$

$\sf \dashrightarrow 2a - (-9) = 5$

$\sf \dashrightarrow 2a + 9 = 5$

$\sf \dashrightarrow 2a = 5 - 9$

$\sf \dashrightarrow 2a = -4$

$\sf \dashrightarrow a = \dfrac{-4}{2}$

$\sf \dashrightarrow a = -2$

Hence, the values of a and b are -2 and -3 respectively.