Question

9. Determine real numbers x and y for which the following equations are true:
(i) 2x + (3x + y) i = 4 + 10i​

Answer 1

$\underline{\sf{\red{Given:-}}}$

• $\sf\ 2x + (3x+y) i = 4 + 10i$

$\underline{\sf{\red{Solution:-}}}$

According to the question:-

$\dashrightarrow\: \sf\ 2x=4, 3x+4y = 10$

$\dashrightarrow\: \sf\ x = \dfrac{4}{2}$

$\dashrightarrow\: \sf\ x= 2$

Now, put value of x in other equation,

$\dashrightarrow\: \sf\ 3(2)+4y=10$

$\dashrightarrow\: \sf\ 6+4y=10$

$\dashrightarrow\: \sf\ 4y =10-6$

$\dashrightarrow\: \sf\ 4y =4$

$\dashrightarrow\: \sf\ y= 1$

Hence proved.

Answer 2

Given Equation

• 2x + (3x + y)i = 4 + 10i

To find

• Value of x and y.

Solution

⌬ On comparing the equation, we get

• 2x = 4
• 3x + y = 10

⌬ Solving both the equation

$\tt:\implies\: \: \: \: \: \: \: \: {2x = 4}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{4}{2}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = 2}$

⠀

⌬ Putting the value of x in second Equation

$\tt:\implies\: \: \: \: \: \: \: \: {3x + y = 10}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {3(2) + y = 10}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {6 + y = 10}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {y = 10 - 6}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {y = 4}$

⠀

⌬ Hence, the value of

• x = 2
• y = 4