Question

Help me please !! i need the answer

Answer 1

`PQ=22\\\\QR=7\\\\PR=29`

Explanation:

To find the value of y, you can create an equation where two parts of the line are equal to the whole line:

`PQ+QR=PR`

Substitute given values:

`(8y+6)+(y+5)=(19y-9)`

Solve for y. Simplify parentheses:

`8y+6+y+5=19y-9`

Combine like terms to simplify the equation:

`8y+y+6+5=19y-9\\\\9y+11=19y-9`

Get the variable on one side of the equation and the constants on the other. Add 9 to both sides:

`9y+11+9=19y-9+9\\\\9y+20=19y`

Subtract 9y from both sides:

`9y-9y+20=19y-9y\\\\20=10y`

Isolate the variable. Divide both sides by 10:

`(20)/(10) =(10y)/(10) \\\\y=2`

The value of y is 2. Insert this value into each line segment value and solve:

`PQ=8(2)+6\\\\PQ=16+6\\\\PQ=22`

`QR=(2)+5\\\\QR=7`

`PR=19(2)-9\\\\PR=38-9\\\\PR=29`

:Done

You can check by using:

`PQ+QR=PR\\\\22+7=29`

This statement is true, so the values are correct.