Question

Solve the following system of equations with the elimination method. Write your answers as an Ordered Pair. If infinitely many solutions exist, enter
(oo). If no solution exists, enter DNE
8y = -3x +30
24y+ 9x= -198

Answer 1

To solve the system of equations using the elimination method, let's first rewrite the two equations in a more standard form.

1. The first equation is given as:
\[
8y = -3x + 30
\]
We can rearrange it to:
\[
3x + 8y = 30 \quad \text{(Equation 1)}
\]

2. The second equation is given as:
\[
24y + 9x = -198 \quad \text{(Equation 2)}
\]

Now we have the system of equations:
\[
\begin{align*}
3x + 8y &= 30 \quad \text{(1)}\\
9x + 24y &= -198 \quad \text{(2)}
\end{align*}
\]

Next, we'll use the elimination method to eliminate one of the variables.

We can multiply Equation (1) by 3 so that the coefficients of \( x \) will match between the two equations:
\[
9x + 24y = 90 \quad \text{(3)}
\]
Now we have the modified system:
\[
\begin{align*}
9x + 24y &= 90 \quad \text{(3)}\\
9x + 24y &= -198 \quad \text{(2)}
\end{align*}
\]

Now we can set the two equations equal to each other:
\[
90 = -198
\]

This is a contradiction, meaning that the two equations represent parallel lines and there is no point that satisfies both equations simultaneously.

Thus, the solution to the system of equations is:
\[
\text{DNE}
\]