Answer:
x=26
w=28
Step-by-step explanation:
If △GHI≅△STR
Then TS = HG, so
-25x+27w-63 = -x +w +41
and HI = RT
w + x -6 = -15w + 18x
Simplifying the equations
w + x -6 = -15w + 18x
Add 15w to each side
w+15w + x -6 = -15w+15w + 18x
16w +x -6 = 18x
Subtract x from each side
16w +x-x -6 = 18x-x
16w-6 = 17x
Simplifying the second equation
-25x+27w-63 = -x +w +41
Add 25x to each side
-25x+25x+27w-63 = -x+25x +w +41
27w-63 = 24x+w+41
Subtract w from each side
27w-w -63 = 24x+41
26w -63 = 24x+41
Subtract 41 from each side
26w -63-41 = 24x
26w -104 = 24x
Now Multiply each equation so we can eliminate x
26w -104 = 24x
16w-6 = 17x
Multiply the first by 17 and the second by -24
442w -1768 = 408x
-384w +144 = -408x
---------------------------------
58w -1624=0
58w = 1624
Divide by 58
58w/58 = 1624/58
w= 28
Now find x
16w -6 =17x
16*28 -6 =17x
442=17x
442/17 =x
26=x
