Solve the following system of equations:

$152x-378y=-74$$-378x+152y=-604$

Given:

The given system of equations is:

$152x-378y=-74$

$-378x+152y=-604$

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

$152x-378y=-74$......(i)

$-378x+152y=-604$.....(ii)

Adding equations (i) and (ii), we get,

$152x-378y-378x+152y=-74-604$

$-226x-226y=-678$

$-226(x+y)=-226\times3$

$x+y=3$.....(iii)

Subtracting equation (ii) from equation (i), we get, 

$152x-378y-(-378x+152y)=-74-(-604)$

$530x-530y=530$

$530(x-y)=530$

$x-y=1$.....(iv)

Adding equations (iii) and (iv), we get,

$x+y+x-y=3+1$

$2x=4$

$x=\frac{4}{2}$

$x=2$

Using $x=2$ in equation (iii), we get,

$2+y=3$

$y=3-2$

$y=1$

Therefore, the solution of the given system of equations is $x=2$ and $y=1$.  

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Updated on: 10-Oct-2022

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