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Use the number line below, where [tex]\( RS = 8y + 2 \)[/tex], [tex]\( ST = 5y + 9 \)[/tex], and [tex]\( RT = 63 \)[/tex].

a. What is the value of [tex]\( y \)[/tex]?
b. Find [tex]\( RS \)[/tex] and [tex]\( ST \)[/tex].

a. What is the value of [tex]\( y \)[/tex]?
[tex]\[ y = \][/tex] (Type an integer or a decimal.)

b. Find [tex]\( RS \)[/tex] and [tex]\( ST \)[/tex].
[tex]\[ RS = \][/tex]
[tex]\[ ST = \][/tex]



Answer :

GinnyAnswer
Let's solve the given problem step-by-step.

1. We have the equations:
[tex]\[ RS = 8y + 2 \][/tex]
[tex]\[ ST = 5y + 9 \][/tex]
[tex]\[ RT = 63 \][/tex]
We know from the number line that:
[tex]\[ RS + ST = RT \][/tex]
Hence, we have:
[tex]\[ 8y + 2 + 5y + 9 = 63 \][/tex]

2. Combine like terms:
[tex]\[ 13y + 11 = 63 \][/tex]

3. Subtract 11 from both sides to isolate the term with [tex]\( y \)[/tex]:
[tex]\[ 13y = 52 \][/tex]

4. Divide both sides by 13 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{52}{13} = 4 \][/tex]

So, the value of [tex]\( y \)[/tex] is [tex]\( 4 \)[/tex].

Next, we need to find the values of RS and ST.

5. Substitute [tex]\( y = 4 \)[/tex] back into the equation for RS:
[tex]\[ RS = 8y + 2 = 8(4) + 2 = 32 + 2 = 34 \][/tex]

6. Substitute [tex]\( y = 4 \)[/tex] back into the equation for ST:
[tex]\[ ST = 5y + 9 = 5(4) + 9 = 20 + 9 = 29 \][/tex]

### Summary of Results:

a. The value of [tex]\( y \)[/tex]:
[tex]\[ y = 4 \][/tex]

b. The values of [tex]\( RS \)[/tex] and [tex]\( ST \)[/tex]:
[tex]\[ RS = 34 \][/tex]
[tex]\[ ST = 29 \][/tex]

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