152x-378y =-74 -378x+152y = -604 Solve …

The given equations are
{tex}152x - 378y = -74{/tex} ...(i)
{tex}-378x + 152y = -604{/tex}. ... (ii)
Clearly, the coefficients of x and y in one equation are interchanged in the other.
Adding (i) and (ii), we get
{tex}(152-378)x + (-378 +152) y = -(74 + 604){/tex}
{tex}\Rightarrow{/tex} {tex}(-226)x + (-226)y = -678{/tex}
{tex}\Rightarrow{/tex} {tex}(-226)(x + y) = -678{/tex}
{tex}\Rightarrow \quad ( x + y ) = \frac { - 678 } { - 226 } \Rightarrow x + y = 3{/tex}. ...(iii)
Subtracting (ii) from (i), we get
{tex}(152 + 378) x + (-378 - 152)y = (-74 + 604){/tex}
{tex}\Rightarrow{/tex}530x - 530y = 530
{tex}\Rightarrow{/tex} 530(x - y) = 530 {tex}\Rightarrow{/tex} x - y = 1. ... (iv)
Adding (iii) and (iv), we get 2x = 4 {tex}\Rightarrow{/tex} x = 2.
Subtracting (iv) from (iii), we get
2y = 2 {tex}\Rightarrow{/tex} y = 1.
Hence, x = 2 and y = 1