Question

reasoning without solving, tell which method you would choose to solve each system: graphing, substitution, or elimination. explain your answer. 17. $y = 2x - 5$ $4y + 8x = 15$ 18. $2y + 7x = 3$ $y - 7x = 9$

Explanation:

For problem 17:

The first equation is already solved for $y$, which makes substitution straightforward. We can directly substitute $y=2x-5$ into the second equation without rearranging terms.

For problem 18:

The coefficients of $x$ in the two equations are $7$ and $-7$, which are additive inverses. Adding the two equations will eliminate the $x$ variable immediately, making elimination the most efficient method.

Answer:

1. Substitution: The first equation is solved for $y$, so we can substitute $y=2x-5$ directly into the second equation.
2. Elimination: The $x$-terms have coefficients that are additive inverses ($7$ and $-7$), so adding the equations will eliminate $x$ easily.