hayleigh101
Answered

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

Verified Answer :

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  \(x\)  here.

Equation 1:  \(2x-3y=3\)

Equation 2:  \(5x-4y=4\)

Solving for \(y\)  in Equation 1 and substituting that into Equation 2 gives us:

\(2x-3y=3\\2x-3=3y\\\frac{2x-3}{3}=y\)

Substituting this expression into Equation 2 and solving for \(x\)  gives us:

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

\(x=0\)  is the solution. Answer choice B is correct.

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