Question

solve the system for x and y, expressing either value in terms of a, if necessary. assume that a ≠ 0.
3ax + 7y = -19
ax + 5y = -17

Explanation:

Step1: Eliminate \( x \) by multiplying the second equation

Multiply the second equation \( ax + 5y = -17 \) by \( 3 \) to get \( 3ax + 15y = -51 \).

Step2: Subtract the first equation from the new equation

Subtract \( 3ax + 7y = -19 \) from \( 3ax + 15y = -51 \):

$$
LATEXBLOCK0
$$

Step3: Solve for \( y \)

Divide both sides by \( 8 \): \( y = \frac{-32}{8} = -4 \).

Step4: Substitute \( y = -4 \) into the second equation to solve for \( x \)

Substitute \( y = -4 \) into \( ax + 5y = -17 \):

$$
LATEXBLOCK1
$$

Since \( a
eq 0 \), divide both sides by \( a \): \( x = \frac{3}{a} \).

Answer:

\( x = \frac{3}{a} \), \( y = -4 \)