Question

which of these strategies would eliminate a variable in the system of equations? \\(\

$$\begin{cases} 5x + 3y = 9 \\\\ 4x - 3y = 9 \\end{cases}$$

\\) choose 1 answer: a subtract the top equation from the bottom equation. b subtract the bottom equation from the top equation. c add the equations.

Explanation:

Step1: Analyze y coefficients

Top equation: $+3y$, Bottom equation: $-3y$

Step2: Test adding equations

$(5x + 3y) + (4x - 3y) = 9 + 9$
$5x+4x+3y-3y=18$
$9x=18$ (y is eliminated)

Step3: Test subtracting options

Subtract top from bottom: $(4x-3y)-(5x+3y)=9-9$ → $-x-6y=0$ (no variable eliminated)
Subtract bottom from top: $(5x+3y)-(4x-3y)=9-9$ → $x+6y=0$ (no variable eliminated)

Answer:

C. Add the equations.