Questions: Which of the following pairs of numbers satisfies the equation 2x+3y=8? A x=1, y=2 B x=2, y=1 C x=-1, y=2 D x -> 2, y=4

Transcript text: Which of the following pairs of numbers satisfies the equation $2 x+3 y=8$ ? A $\left\{\begin{array}{l}x=1 \\ y=2\end{array}\right.$ B $\left\{\begin{array}{l}x=2 \\ y=1\end{array}\right.$ C $\quad\left\{\begin{array}{l}x=-1 \\ y=2\end{array}\right.$ D $\quad\left\{\begin{array}{l}x \leadsto 2 \\ y=4\end{array}\right.$

Solution

Solution Steps

To determine which pair of numbers satisfies the equation $2x + 3y = 8$, we will substitute each pair of values for $x$ and $y$ into the equation and check if the equation holds true. We will iterate through each option and verify the result.

Step 1: Substitute Values for Option A

For option A, we have $ x = 1 $ and $ y = 2 $. Substituting these values into the equation $ 2x + 3y $:

\[ 2(1) + 3(2) = 2 + 6 = 8 \]

Step 2: Substitute Values for Option B

For option B, we have $ x = 2 $ and $ y = 1 $. Substituting these values into the equation:

\[ 2(2) + 3(1) = 4 + 3 = 7 \]

Step 3: Substitute Values for Option C

For option C, we have $ x = -1 $ and $ y = 2 $. Substituting these values into the equation:

\[ 2(-1) + 3(2) = -2 + 6 = 4 \]

Step 4: Substitute Values for Option D

For option D, we have $ x = 2 $ and $ y = 4 $. Substituting these values into the equation:

\[ 2(2) + 3(4) = 4 + 12 = 16 \]