Explanation:
2 equations with 2 variables.
either we use 1 equation to express 1 variable by the other and bring this into the second equation to solve for the second variable.
or we do equation arithmetic (subtract one equation from the other so that one variable disorders in the result, and solve for the remaining variable).
since the factors and constants don't seem to be multiples or share nice factors with each other, I suggest the second way.
7x - 4y = 37
6x + 3y = 51
multiply the first equating by 3, and the second one by 4, and then add both equations :
21x - 12y = 111
24x + 12y = 204
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45x + 0 = 315
x = 7
then we use one of the original equations to get y :
7×7 - 4y = 37
49 - 4y = 37
12 = 4y
y = 3