Question

Quesheip Use the number line below, where RS = 6y +2, ST=5y + 9, and RT= 13y - 1 a What is the value of y? b Find RS, ST, and RT. R S T a. What is the value of y? y=Type an integer or a decimal.)
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Answer 1

Answer:

$y = 6$

$RS = 38$

$ST = 39$

$RT = 77$

Step-by-step explanation:

Given:

$RS = 6y +2$

$ST=5y + 9$

$RT= 13y - 1$

Solving (a): The value of y

From the given parameters, we understand that

$RT = RS + ST$

Substitute values for RS, ST and RT

$13y - 1 = 6y + 2 + 5y + 9$

Collect Like Terms

$13y - 6y - 5y = 1 + 2 + 9$

$2y = 12$

Divide both sides by 2

$y = \frac{12}{2}$

$y = 6$

Solving (b):

The value of RS

Substitute 6 for y in $RS = 6y +2$

$RS = 6 * 6 + 2$

$RS = 36 + 2$

$RS = 38$

The value of ST

Substitute 6 for y in $ST=5y + 9$

$ST = 5 * 6 + 9$

$ST = 30 + 9$

$ST = 39$

The value of ST

Substitute 6 for y in $RT= 13y - 1$

$RT = 13 * 6 - 1$

$RT = 78 - 1$

$RT = 77$