Question

What is the value of the x variable in the solution to the following system of equations?2x − 3y = 35x − 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

Step-by-step explanation

Given the system of equations:

(1) 2x -3y = 3

(2) 5x -4y = 4

Isolating x from (1):

`2x\text{ = 3 + 3y}`

Dividing both sides by 2:

`x=(3+3y)/(2)`
`\mathrm{Substitute\: }x=(3+3y)/(2)`
`\begin{bmatrix}5\cdot(3+3y)/(2)-4y=4\end{bmatrix}`

Simplifying the expression:

`\begin{bmatrix}(15+7y)/(2)=4\end{bmatrix}`

Multiplying both sides by 2:

`15+7y=2\cdot4`

Multiplying numbers:

`15+7y=8`

Subtracting -15 to both sides:

`7y=8-15`

Dividing both sides by 7:

`y=(8-15)/(7)`

Simplifying:

`y=-1`

Plugging in y= -1 into (1):

`x=(3+3\left(-1\right))/(2)`

Multiplying and adding numbers:

`x=(0)/(2)=0`

In conclusion, the value of x in the system of equations is x=0