What is the value of the x variable in the solution to the following system of equations?

4x − 3y = 3

5x − 4y = 3 (5 points)

x can be any number as there are infinitely many solutions to this system

there is no x value as there is no solution to this system

−3

3

4x - 3y = 3...multiply by 4

5x - 4y = 3...multiply by -3

16x - 12y = 12 (result of multiplying by 4)

-15x + 12y = - 9 (result of multiplying by -3)

add

x = 3

4x - 3y = 3

4(3) - 3y = 3

12 - 3y = 3

-3y = 3 - 12

-3y = - 9

y = -9/-3

y = 3

solution is (3,3)and the x = 3

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 :

[tex]4x-3y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x-4y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

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

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

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

[tex](16x-12y)-(15x-12y)=12-9\\\\\Rightarrow x=3.[/tex]

Thus, the required value of variable x is 3.

Since boh equal 3, set each to each other

4x-3y=5x-4y

minus 4x both sides

-3y=x-4y

add 4y to both sides

y=x

now sub that

4x-3y=3

4x-3x=3

x=3

x=y

y=3

x=3=y

the solution is (3,3)

There is no x value as there is no solution. I plugged into desmos cause it didnt make sense at first then it showed me that it has no solution.

I hope this helps you

[tex]What is the value of the x variable in the solution to the following system of equations? 4x − 3y =[/tex]

We multiply both equations by a constant term so that when we subtract the equations, the y values cancel out:

4(4x - 3y = 3)

3(5x - 4y = 3)

16x - 12y = 12

15x -12y = 9; subtracting the second equation from the first:

x = 3

hello :

4x − 3y = 3 ...(1)

5x − 4y = 3 ...(2)

by (1) : 3y = 4x-3

y = (4/3)x -1 ...(*)

by (2) : 4y = 5x-3

y = (5/4)x -3/4 ... (**)

by (*) (**) ;

(4/3)x -1 =(5/4)x -3/4

(4/3)x-(5/4)x=1-3/4

(16x-15x)/12 =1/4 = 3/12

x=3

Solve 4x − 3y = 3 and 5x − 4y = 3

Step 1: Solve for x in 4x-3y=3:

4x-3y=3

4x-3y+3y=3+3y [Add 3y to both sides]

4x=3y+3

[tex]\frac{4x}{4} = \frac{3x+3}{4}[/tex] [Divide both sides by 4]

x=[tex]\frac{3}{4}y+ \frac{3}{4}[/tex]

Step 2: Substitute [tex]\frac{3}{4}y+ \frac{3}{4}[/tex] for x in 5x-4y=3

5x-4y=3

5([tex]\frac{3}{4}y+ \frac{3}{4}[/tex])-4y=3

[tex]\frac{-1}{4}y+ \frac{15}{4} =3[/tex]

[tex]\frac{-1}{4}y+ \frac{15}{4} - \frac{15}{4} =3- \frac{15}{4}[/tex] [Subtract [tex]\frac{15}{4}[/tex] to both sides]

[tex]\frac{-1}{4}y= \frac{-3}{4}[/tex]

[tex]\frac{ \frac{-1}{4}y}{ \frac{-1}{4} }= \frac{\frac{-3}{4} }{ \frac{-1}{4}}[/tex] [Divide both sides by [tex]\frac{-1}{4}[/tex] ]

y = 3

Step 3: Substitute 3 for y in x = [tex]\frac{3}{4}y+ \frac{3}{4}[/tex]

[tex]\frac{3}{4}y+ \frac{3}{4}[/tex]

[tex]\frac{3}{4}(3)+ \frac{3}{4}[/tex]

x = 3

4x - 3y = 3 (x-4)

5x - 4y = 3 (x3)

-16x + 12y = -12

15x -12y = 9

-x = -3

x = 3

The two equations given in the question are

4x _ 3y = 3

And

5x _ 4y = 3

Multiplying the first equation by 4 and the second equation by 3, we get

16x - 12y = 12

15x - 12y = 9

Subtracting the second equation from the first equation, we get

x = 3

I hope the above procedure is clear enough for you to understand. I hope that this is the answer that you were looking for and the answer has actually come to your great help.