Question

What is the value of the x variable in the solution to the following system of equations? 4x − 3y = 3 5x − 4y = 3

Answer 1

4x - 3y = 3 (x-4)
5x - 4y = 3 (x3)
-16x + 12y = -12
15x -12y = 9
-x = -3
x = 3

Answer 2

Answer:  The required value of variable x is 3.

Step-by-step explanation:  We are given to find the value of the variable x in the solution to the following system of equations :

$4x-3y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x-4y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

In order to find the value of x, we need to eliminate y from both the equations.

Multiplying equation (i) by 4 and equation (ii) by 3, we have

$4(4x-3y)=4\times 3\\\\\Rightarrow 16x-12y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)\\\\\\3(5x-4y)=3\times3\\\\\Rightarrow 15x-12y=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

Subtracting equation (iv) from equation (iii), we get

$(16x-12y)-(15x-12y)=12-9\\\\\Rightarrow x=3.$

Thus, the required value of variable x is 3.