Answer:
[tex]PQ=22\\\\QR=7\\\\PR=29[/tex]
Step-by-step explanation:
To find the value of y, you can create an equation where two parts of the line are equal to the whole line:
[tex]PQ+QR=PR[/tex]
Substitute given values:
[tex](8y+6)+(y+5)=(19y-9)[/tex]
Solve for y. Simplify parentheses:
[tex]8y+6+y+5=19y-9[/tex]
Combine like terms to simplify the equation:
[tex]8y+y+6+5=19y-9\\\\9y+11=19y-9[/tex]
Get the variable on one side of the equation and the constants on the other. Add 9 to both sides:
[tex]9y+11+9=19y-9+9\\\\9y+20=19y[/tex]
Subtract 9y from both sides:
[tex]9y-9y+20=19y-9y\\\\20=10y[/tex]
Isolate the variable. Divide both sides by 10:
[tex]\frac{20}{10} =\frac{10y}{10} \\\\y=2[/tex]
The value of y is 2. Insert this value into each line segment value and solve:
[tex]PQ=8(2)+6\\\\PQ=16+6\\\\PQ=22[/tex]
[tex]QR=(2)+5\\\\QR=7[/tex]
[tex]PR=19(2)-9\\\\PR=38-9\\\\PR=29[/tex]
:Done
You can check by using:
[tex]PQ+QR=PR\\\\22+7=29[/tex]
This statement is true, so the values are correct.
