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

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=\frac{3+3y}{2}$$\mathrm{Substitute\: }x=\frac{3+3y}{2}$$\begin{bmatrix}5\cdot\frac{3+3y}{2}-4y=4\end{bmatrix}$

Simplifying the expression:

$\begin{bmatrix}\frac{15+7y}{2}=4\end{bmatrix}$

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:

$y=\frac{8-15}{7}$

Simplifying:

$y=-1$

Plugging in y= -1 into (1):

$x=\frac{3+3\left(-1\right)}{2}$

Multiplying and adding numbers:

$x=\frac{0}{2}=0$

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