Question

renee wants to solve the system of equations. which number can she multiply the first equation by so that when the two equations are added together, the y term is eliminated? \\(\frac{2}{5}x + \frac{1}{5}y = 8\\) \\(\frac{1}{6}x - 3y = 8\\) \\(circ -15\\) \\(circ -5\\) \\(circ 5\\) \\(circ 15\\)

Explanation:

Step1: Identify y coefficients

First equation y-term: $\frac{1}{5}y$; Second equation y-term: $-3y$

Step2: Set up elimination condition

Let multiplier be $k$. Need $k \cdot \frac{1}{5}y + (-3y) = 0$

Step3: Solve for k

$\frac{k}{5} - 3 = 0$
$\frac{k}{5} = 3$
$k = 3 \times 5 = 15$

Answer:

15