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

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

## This Post Has 10 Comments

1. hardwick744 says:

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)
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

2. destinywiggins75 says:

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.

3. anjumuddin9 says:

Since boh equal 3, set each to each other
4x-3y=5x-4y
minus 4x both sides
-3y=x-4y
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)

4. tyheath42 says:

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.

5. rayne40 says:

I hope this helps you
$What is the value of the x variable in the solution to the following system of equations? 4x − 3y =$

6. lizzyhearts says:

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

7. littleprinces says:

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

8. yungmoney30 says:

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
$\frac{4x}{4} = \frac{3x+3}{4}$ [Divide both sides by 4]
x=$\frac{3}{4}y+ \frac{3}{4}$

Step 2: Substitute $\frac{3}{4}y+ \frac{3}{4}$ for x in 5x-4y=3
5x-4y=3
5($\frac{3}{4}y+ \frac{3}{4}$)-4y=3
$\frac{-1}{4}y+ \frac{15}{4} =3$
$\frac{-1}{4}y+ \frac{15}{4} - \frac{15}{4} =3- \frac{15}{4}$ [Subtract $\frac{15}{4}$ to both sides]
$\frac{-1}{4}y= \frac{-3}{4}$
$\frac{ \frac{-1}{4}y}{ \frac{-1}{4} }= \frac{\frac{-3}{4} }{ \frac{-1}{4}}$ [Divide both sides by $\frac{-1}{4}$ ]
y = 3

Step 3: Substitute 3 for y in x = $\frac{3}{4}y+ \frac{3}{4}$
$\frac{3}{4}y+ \frac{3}{4}$
$\frac{3}{4}(3)+ \frac{3}{4}$
x = 3

9. romerok568 says:

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

10. zubaira5798 says:

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.