Question

Question was provided via image upload.

Explanation:

Step1: Identify the system of equations

From the image, the system of linear equations seems to be:
\( 3x + y = 4 \) (let's call this Equation 1)
\( 4x + y = 2 \) (let's call this Equation 2)

Step2: Subtract Equation 1 from Equation 2

Subtracting Equation 1 from Equation 2 to eliminate \( y \):
\( (4x + y) - (3x + y) = 2 - 4 \)
Simplify the left - hand side: \( 4x + y - 3x - y=x \)
Simplify the right - hand side: \( 2 - 4=-2 \)
So, \( x=-2 \)

Step3: Substitute \( x = - 2 \) into Equation 1

Substitute \( x=-2 \) into \( 3x + y = 4 \):
\( 3\times(-2)+y = 4 \)
\( -6 + y = 4 \)
Add 6 to both sides of the equation: \( y=4 + 6=10 \)

Wait, but there are also some dummy variables \( \text{mx} \) and \( \text{my} \) (maybe a typo, perhaps \( \text{mx} \) and \( \text{my} \) are related to some matrix or another method). If we consider the values \( \text{mx}=\frac{2}{3} \) and \( \text{my} = 2 \) (maybe from a different approach like matrix row operations or substitution with different variables). Let's re - examine.

If we consider the two equations as:
Equation 1: \( 3x + y=4 \)
Equation 2: \( 4x + y = 2 \)

Using the elimination method:
Subtract Equation 1 from Equation 2:
\( (4x + y)-(3x + y)=2 - 4\)
\(x=-2\)
Substitute \( x = - 2 \) into Equation 1:
\(3\times(-2)+y = 4\)
\(y=4 + 6 = 10\)

But if we consider the dummy variables (maybe a mis - written system, perhaps the equations are \( 3x+y = 4 \) and \( 4x + y=2 \) with some other variable representation). If we assume that the "dummy variables" are part of a different approach, but the standard solution for the system \(

$$\begin{cases}3x + y=4\\4x + y = 2\end{cases}$$

\) is \( x=-2,y = 10 \)

Answer:

The solution of the system of linear equations \(

$$\begin{cases}3x + y=4\\4x + y = 2\end{cases}$$

\) is \( x=-2,y = 10 \)