Question

Solve: 4x-3y=16,. 6x+5y=62.​

Answer 1

Answer:

Solve equation [2] for the variable x

[2] 6x = 5y + 62

[2] x = 5y/6 + 31/3

// Plug this in for variable x in equation [1]

[1] 4•(5y/6+31/3) - 3y = 16

[1] y/3 = -76/3

[1] y = -76

// Solve equation [1] for the variable y

[1] y = - 76

// By now we know this much :

x = 5y/6+31/3

y = -76

// Use the y value to solve for x

x = (5/6)(-76)+31/3 = -53

(x,y) =(-53,-76)

Answer 2

Answer

$\sf \dashrightarrow 4x - 3y = 16 \: \: --- (i)$

$\sf \dashrightarrow 6x + 5y = 62 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 4x - 3y = 16$

$\sf \dashrightarrow 4x = 16 + 3y$

$\sf \dashrightarrow x = \dfrac{16 + 3y}{4}$

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

$\sf \dashrightarrow 6x + 5y = 62$

$\sf \dashrightarrow 6 \bigg( \dfrac{16 + 3y}{4} \bigg) + 5y = 62$

$\sf \dashrightarrow \dfrac{96 + 18y}{4} + 5y = 62$

$\sf \dashrightarrow \dfrac{96 + 18y + 20y}{4} = 62$

$\sf \dashrightarrow \dfrac{96 + 38y}{4} = 62$

$\sf \dashrightarrow 96 + 38y = 62 \times 4$

$\sf \dashrightarrow 96 + 38y = 248$

$\sf \dashrightarrow 38y = 248 - 96$

$\sf \dashrightarrow 38y = 152$

$\sf \dashrightarrow y = \dfrac{152}{38}$

$\sf \dashrightarrow y = 4$

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

$\sf \dashrightarrow 4x - 3y = 16$

$\sf \dashrightarrow 4x - 3(4) = 16$

$\sf \dashrightarrow 4x - 12 = 16$

$\sf \dashrightarrow 4x = 16 + 12$

$\sf \dashrightarrow 4x = 28$

$\sf \dashrightarrow x = \dfrac{28}{4}$

$\sf \dashrightarrow x = 7$

Hence, the values of x and y are 7 and 4 respectively.