Question

Solve the following systems of equations:
152x - 378y = -74
-378x + 152y = -604

Answer 1

Hint – In this question simply add the two given equations and then divide by -226 all throughout, then we will be getting the value of x in terms of y. Substitute it back to any one of the equation given to get the values.

Complete Step-by-Step solution:
Given system of equations:
$152x - 378y = - 74$............................. (1)
$ - 378x + 152y = - 604$..................... (2)
Now add these two equations we have,
$ \Rightarrow 152x - 378y - 378x + 152y = - 74 - 604$
$ \Rightarrow - 226x - 226y = - 678$
Now divide by -226 throughout we have,
$ \Rightarrow x + y = \dfrac{{ - 678}}{{ - 226}} = 3$
$ \Rightarrow x = 3 - y$......................... (3)
Now substitute this value in equation (1) we have,
$ \Rightarrow 152\left( {3 - y} \right) - 378y = - 74$
Now simplify this equation we have,
$ \Rightarrow 152 \times 3 - 152y - 378y = - 74$
$ \Rightarrow - 530y = - 74 - 456 = - 530$
Now divide by -530 we have,
$ \Rightarrow y = \dfrac{{ - 530}}{{ - 530}} = 1$
Now from equation (3) we have,
$ \Rightarrow x = 3 - \left( 1 \right) = 2$
So the required solution of the given system of equation is
$ \Rightarrow \left( {x,y} \right) = \left( {2,1} \right)$
So this is the required answer.

Note – This question could have been solved by another method in this simply we would be using a substitution method, using the first relation take out x in terms of y and put this relation back into the second equation, to get the value of the unknown variable. This method would be lengthy, therefore before applying this the equations are simplified by addition of them.