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The system of equations

[tex]\[
\left\{
\begin{array}{l}
d = 18t + 34 \\
d = 22t
\end{array}
\right.
\][/tex]

can be used to represent the situation.

a. Solve the system of equations. Which of the following is the solution to the system equations? Select one.

A. [tex]\((5.5, 121)\)[/tex]
B. [tex]\((8.5, 187)\)[/tex]
C. [tex]\((17, 374)\)[/tex]
D. [tex]\((34, 748)\)[/tex]


Sagot :

To solve the system of equations:

[tex]\[ \begin{cases} d = 18t + 34 \\ d = 22t \end{cases} \][/tex]

we can use substitution or elimination. Here, we'll use substitution methodology to find the values of [tex]\( d \)[/tex] and [tex]\( t \)[/tex] that make both equations true simultaneously.

### Step-by-Step Solution:

1. Set the equations equal to each other:

Since both expressions equal [tex]\( d \)[/tex], we can set them equal to each other:
[tex]\[ 18t + 34 = 22t \][/tex]

2. Solve for [tex]\( t \)[/tex]:

To isolate [tex]\( t \)[/tex], subtract [tex]\( 18t \)[/tex] from both sides of the equation:
[tex]\[ 34 = 22t - 18t \][/tex]
Simplify the right side:
[tex]\[ 34 = 4t \][/tex]

Now, divide both sides by 4 to solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{34}{4} = 8.5 \][/tex]

3. Substitute [tex]\( t \)[/tex] back to find [tex]\( d \)[/tex]:

Use the value of [tex]\( t = 8.5 \)[/tex] in either of the original equations to find [tex]\( d \)[/tex]. We'll use [tex]\( d = 22t \)[/tex]:
[tex]\[ d = 22 \times 8.5 = 187 \][/tex]

So, the solution to the system of equations is:
[tex]\[ \boxed{(8.5, 187)} \][/tex]

### Verification with Options:

Now let's compare this solution with the given options to find the correct one:

- Option A: [tex]\((5.5, 121)\)[/tex]
- Option B: [tex]\((8.5, 187)\)[/tex]
- Option C: [tex]\((17, 374)\)[/tex]
- Option D: [tex]\((34, 748)\)[/tex]

Comparing our result [tex]\((8.5, 187)\)[/tex] with the options, we see that:

[tex]\[ \boxed{B. (8.5, 187)} \][/tex]

is the correct answer.