4x + 5y = 812
x + y = 186

Solve using elimination:

|   4   5   |   812 |
|   1   1   |   186 |

R1+ (4x)R2 = R2

|   4   5   |   812 |
|  -4  -4   |  -744 |
-
|   0   1   |   68  |

SO... 1y = 68 ...y=68

back substitute

x = 118