Question

how can you eliminate the x-terms in this system?
4y + 3x = -6
y - x = -5
multiply by 3 on both sides.
multiply the second equation by 3.
3(y - x) = 3(-5)
y -? x = -15

Explanation:

Step1: Identify the second equation

The second equation is \( y - x = -5 \).

Step2: Multiply both sides by 3

To eliminate the \( x \)-terms, we multiply the second equation \( y - x = -5 \) by 3. Using the distributive property, we get \( 3(y - x)=3\times(-5) \). Simplifying the left side: \( 3y - 3x = -15 \). Now, the first equation is \( 4y + 3x = -6 \) and the modified second equation is \( 3y - 3x = -15 \). If we add these two equations, the \( x \)-terms (\( +3x \) and \( -3x \)) will cancel out.

Answer:

To eliminate the \( x \)-terms, multiply the second equation \( y - x = -5 \) by 3, resulting in \( 3y - 3x = -15 \). Then, add this new equation to the first equation \( 4y + 3x = -6 \), and the \( x \)-terms will be eliminated.