Question

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

Answer 1

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)
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- 7x = 0
x = 0 <===

Answer 2

B

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\\(2x-3)/(3)=y`

Substituting this expression into Equation 2 and solving for
`x` gives us:

`5x-4((2x-3)/(3))=4\\5x-((8x-12)/(3))=4\\(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.