Certainly! Let's solve the given system of equations step-by-step as per the specified multiplications:
[tex]\[
\begin{array}{l}
4x + 9y = 21 \quad \text{(Equation 1)} \\
3x - 8y = 1 \quad \text{(Equation 2)}
\end{array}
\][/tex]
Step 1: Multiply the first equation by 3 and the second equation by 4.
For the first equation:
[tex]\[
3 \cdot (4x + 9y) = 3 \cdot 21 \\
12x + 27y = 63
\][/tex]
For the second equation:
[tex]\[
4 \cdot (3x - 8y) = 4 \cdot 1 \\
12x - 32y = 4
\][/tex]
We now have:
[tex]\[
\begin{array}{l}
12x + 27y = 63 \\
12x - 32y = 4
\end{array}
\][/tex]
Step 2: Multiply the first equation by -3 and the second equation by -4.
For the first equation:
[tex]\[
-3 \cdot (4x + 9y) = -3 \cdot 21 \\
-12x - 27y = -63
\][/tex]
For the second equation:
[tex]\[
-4 \cdot (3x - 8y) = -4 \cdot 1 \\
-12x + 32y = -4
\][/tex]
We now have:
[tex]\[
\begin{array}{l}
-12x - 27y = -63 \\
-12x + 32y = -4
\end{array}
\][/tex]
Step 3: Multiply the first equation by 8 and the second equation by 9.
For the first equation:
[tex]\[
8 \cdot (4x + 9y) = 8 \cdot 21 \\
32x + 72y = 168
\][/tex]
For the second equation:
[tex]\[
9 \cdot (3x - 8y) = 9 \cdot 1 \\
27x - 72y = 9
\][/tex]
We now have:
[tex]\[
\begin{array}{l}
32x + 72y = 168 \\
27x - 72y = 9
\end{array}
\][/tex]
Step 4: Multiply the first equation by -3 again and the second equation by 4.
For the first equation:
[tex]\[
-3 \cdot (4x + 9y) = -3 \cdot 21 \\
-12x - 27y = -63
\][/tex]
For the second equation:
[tex]\[
4 \cdot (3x - 8y) = 4 \cdot 1 \\
12x - 32y = 4
\][/tex]
We now have:
[tex]\[
\begin{array}{l}
-12x - 27y = -63 \\
12x - 32y = 4
\end{array}
\][/tex]
By carefully following the specified multiplications, we reach the results:
[tex]\[
(12, 27, 63, 12, -32, 4, -12, -27, -63, -12, 32, -4, 32, 72, 168, 27, -72, 9, -12, -27, -63, 12, -32, 4)
\][/tex]
