hayleigh101
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What is the value of the x variable in the solution to the following system of equations?. .
2x − 3y = 3
5x − 4y = 4
A.) −1
B.) 0
C.) x can be any number as there are infinitely many solutions to this system
D.) There is no x value as there is no solution to this system

Respuesta :

texaschic101
2x - 3y = 3.....multiply by 4
5x - 4y = 4....multiply by -3
--------------
8x - 12y = 12 (result of multiplying by 4)
-15x + 12y = -12 (result of multiplying by -3)
-------------
- 7x = 0
x = 0 <===
TaeKwonDoIsDead

Answer:

B


Step-by-step explanation:


We need to solve for  [tex]x[/tex]  here.

Equation 1:  [tex]2x-3y=3[/tex]

Equation 2:  [tex]5x-4y=4[/tex]

Solving for [tex]y[/tex]  in Equation 1 and substituting that into Equation 2 gives us:

[tex]2x-3y=3\\2x-3=3y\\\frac{2x-3}{3}=y[/tex]

Substituting this expression into Equation 2 and solving for [tex]x[/tex]  gives us:

[tex]5x-4(\frac{2x-3}{3})=4\\5x-(\frac{8x-12}{3})=4\\\frac{15x-8x+12}{3}=4\\15x-8x+12=12\\7x+12=12\\7x=0\\x=0[/tex]

[tex]x=0[/tex]  is the solution. Answer choice B is correct.

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