To calculate: The solution for the system of equations 7\left(x-y\r

Given Information:
The provided system of equations is ${\displaystyle 7(x-y)=3-5x}$ and ${\displaystyle 4(3x-y)=-2x}$.
Formula used:
Solving a System of Equations by Using the Addition Method:
Step1: Write both equations in standard form: ${\displaystyle Ax+By=C}$
Step2: Clear fractions or decimals.
Step3: Multiply one or both equations by nonzero constants to create
opposite coefficients for one of the variables.
Step4: Add the equations from step3 to eliminate one variable.
Step5: Solve for the remaining variable.
Step6: Substitute the known value found in step5 into one of the original equations to solve for the other variable.
Step7: Check the ordered pair in each equation and write the solution set.
Calculation:
Consider the provided system of equations, ${\displaystyle 7(x-y)=3-5x}$ and ${\displaystyle 4(3x-y)=-2x}$
Convert the equations into standard form ${\displaystyle Ax+By=C}$:
${\displaystyle 7(x-y)=3-5x}$
${\displaystyle 7x-7y=3-5x}$ ............(1)
${\displaystyle 7x-2y=3}$
And,
${\displaystyle 4(3x-y)=-2x}$
${\displaystyle 12x-4y=-2x}$............(2)
${\displaystyle 14x-4y=-0}$
Now, multiply by —2 in the equation (1):
$-14x+4y=-6$............(3)
Now, add equations (2) and (3):
${\displaystyle 14x—4y=0}$
${\displaystyle -l4x+dy=-6}$
${\displaystyle \overline{0=-6}}$
The system of equations is reduced to a contradiction. Hence, the system is inconsistent.
Therefore, the solution for the system of equations ${\displaystyle 7(x-y)=3-5x}$ yand ${\displaystyle 4(3x-y)=-2x}$ is {} and the system is inconsistent.