Question

Given the system of equations below:
3x-2y=10
3x+2y=14
Part III: You solved this system by eliminating the
-terms. Dylan wants to eliminate the
-terms instead. What do they need to do as their first step? (You are NOT required to solve anything here.)

Answer 1

To eliminate the \( x \)-terms from the given system of equations, Dylan can modify the equations to make the coefficients of \( x \) in both equations equal. The system of equations is:

1. \( 3x - 2y = 10 \)
2. \( 3x + 2y = 14 \)

Since the coefficients of \( x \) in both equations are already the same (3), Dylan can simply subtract one equation from the other to eliminate the \( x \)-terms.

However, if Dylan wants to explicitly eliminate the \( x \)-terms by getting them to the same side first, the first step they can take is to rewrite one of the equations in terms of \( 3x \) and align the equations appropriately.

For example, they could modify the equations as follows:

1. From the first equation, express \( 3x \):
\[
3x = 2y + 10
\]
2. From the second equation, express \( 3x \):
\[
3x = -2y + 14
\]

After this adjustment, they can set the two expressions for \( 3x \) equal to each other to eliminate \( x \).

So, the first step is: **Rewrite the equations to express \( 3x \) in terms of \( y \) for both equations.**