Given

[1]#color(white)("XXX")16x+3y=7#

[2]#color(white)("XXX")9x+5y=-12#

Multiply [1] by #5# and [2] by #3# to get equations with equal coefficients for #y#

[3]#color(white)("XXX")80x+15y=35#

[4]#color(white)("XXX")27x+15y=-36#

Subtract [4] from [3]

[5]#color(white)("XXX")53x=71#

Divide by #23#

[6]#color(white)("XXX")x=71/53#

#color(white)("XXX")#Yes; it's going to be ugly; but that doesn't mean it's going to be wrong.

Substitute #71/53# for #x# in [1]

[7]#color(white)("XXX")(16xx71)/53+3y=7#

Simplify

[8]#color(white)("XXX")1136/53+159/53y=371/53#

[9]#color(white)("XXX")159y=-765#

[10]#color(white)("XXX")y=-765/159=-255/23#

I would (strongly) recommend using a calculator or spreadsheet to verify these values in the original equations.