Verified Answer :

luana

\(RS+ST=RT\\\\ RS=8y+4\\ RT=15y-9\\ ST=4y+8\\\\ 8y+4+4y+8=15y-9\\ 12y+12=15y-9\ \ \ |Subtract\\ 12y=15y-9-12\\ 12y=15y-21\ \ \ | Subtract\ 15y\\ 12y-15y=-21\\ -3y=-21 \ \ |Divide\ by\ (-3)\\ y=7\\\\ RS=8y+4=8*7+4=56+4=60\\ RT=15y-9=15*7-9=105-9=96\\ ST=4y+8=4*7+8=28+8=36\)

emmaegg

First write your equation to solve for y. You know RS plus ST equals RT. 
8y + 4 + 4y + 8 = 15y - 9

Next combine like terms on the left side of the equal sign. 
8y + 4y + 4 + 8 = 15y - 9
 
Then add the like terms.
12y + 12 = 15y - 9

Simplify using algebra. Subtract 12y from both sides. 
12y + 12 = 15y - 9
-12y          -12y
12 = 3y - 9

Now add 9 to both sides.
12 = 3y - 9
+9          +9
21 = 3y

Divide both sides by 3. Now you have your y value.
21 = 3y
/3     /3
7 = y

Now that you have the y value (7), just plug it into the equations for each side. 

RS:
8y + 4
8 7 +4
56 + 4
60
RS = 60

ST:
4y + 8 
4 7 +8
28 + 8
29
ST = 36

RT:
15y - 9
15 * 7 - 9
105 - 9
96
RT = 96

We know these are correct because RS + ST should equal RT. Does 60 + 36 = 96? Yes. 

Hope this was of help!




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