Question

If 4x-3y=1 and 5x-7y=-2 then 3x+4y is

Answer 1

Step-by-step explanation:

20x-15y=5

20x-28y=-8

now subtract both equation

13y=13

y=1

20x-15=5

20x=20

x=1

Hence, 3*1+4*1=7

Answer 2

Answer

$\sf \dashrightarrow 4x - 3y = 1 \: \: --- (i)$

$\sf \dashrightarrow 5x - 7y = -2 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 4x - 3y = 1$

$\sf \dashrightarrow 4x = 1 + 3y$

$\sf \dashrightarrow x = \dfrac{1 + 3y}{4}$

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

$\sf \dashrightarrow 5x - 7y = -2$

$\sf \dashrightarrow 5 \bigg( \dfrac{1 + 3y}{4} \bigg) - 7y = -2$

$\sf \dashrightarrow \dfrac{5 + 15y}{4} - 7y = -2$

$\sf \dashrightarrow \dfrac{5 + 15y - 28y}{4} = -2$

$\sf \dashrightarrow \dfrac{5 - 13y}{4} = -2$

$\sf \dashrightarrow 5 - 13y = -2 \times 4$

$\sf \dashrightarrow 5 - 13y = -8$

$\sf \dashrightarrow -13y = -8 - 5$

$\sf \dashrightarrow -13y = -13$

$\sf \dashrightarrow y = \dfrac{-13}{-13}$

$\sf \dashrightarrow y = 1$

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

$\sf \dashrightarrow 4x - 3y = 1$

$\sf \dashrightarrow 4x - 3(1) = 1$

$\sf \dashrightarrow 4x - 3 = 1$

$\sf \dashrightarrow 4x = 1 + 3$

$\sf \dashrightarrow 4x = 4$

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

$\sf \dashrightarrow x = 1$

Now, let's find the answer of this question.

$\sf \dashrightarrow 3x + 4y$

$\sf \dashrightarrow 3(1) + 4(1)$

$\sf \dashrightarrow 3 + 4$

$\sf \dashrightarrow 7$

Hence, the value of 3x+4y is 7.