7x+1y = 17.00 can be simplified to y = -7x +17
-7x +17 can then be substituted for y in 3x+ 4y =17.50
3x+4(y) = 17.50
3x+ 4(-7x +17) = 17.50
From here you can solve for X
3x + 4(-7x +17) = 17.50
3x -28x + 68 = 17.50
-25x + 68 = 17.50
-68 -68
-25x = -50.50
÷-25 ÷-25
X = 2.02
You can then replace x with 2.02 in the original 7x + 1y = 17.00 to solve for y.
7(x) + 1y = 17.00
7(2.02) + y = 17.00
14.14 + y = 17.00
-14.14 -14.14
y = 2.86
Then substitute 2.02 for x and 2.86 for y in the original 3x+ 4y = 17.50 to check.
3(x) + 4(y) = 17.50
3(2.02) + 4(2.86) = 17.50
6.06 + 11.44 = 17.50
17.50 = 17.50
So
X = 2.02
and
Y = 2.86
or the solution set is (2.02, 2.86)
Hope this helps