Step 1) Solve the first equation for #x#:
#x + 3y = 97#
#x + 3y - color(red)(3y) = 97 - color(red)(3y)#
#x + 0 = 97 - 3y#
#x = 97 - 3y#
Step 2) Substitute #(97 - 3y)# for #x# in the second equation and solve for #y#:
#43x - 19y = 105# becomes:
#43(97 - 3y) - 19y = 105#
#(43 * 97) - (43 * 3y) - 19y = 105#
#4171 - 129y - 19y = 105#
#4171 - 148y = 105#
#-color(red)(4171) + 4171 - 148y = -color(red)(4171) + 105#
#0 - 148y = -4066#
#-148y = -4066#
#(-148y)/color(red)(-148) = (-4066)/color(red)(-148)#
#(color(red)(cancel(color(black)(-148)))y)/cancel(color(red)(-148)) = 2033/74#
#y = 2033/74#
Step 3) Substitute #2033/74# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 97 - 3y# becomes:
#x = 97 - (3 * 2033/74)#
#x = 97 - 6099/74#
#x = (74/74 xx 97) - 6099/74#
#x = 7178/74 - 6099/74#
#x = 1079/74#
The solution is: #x = 1079/74# and #y = 2033/74# or #(1079/74, 2033/74)#
