Question

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

Explanation:

Step1: Identify x - coefficients

The system is:

1. \(4y + 3x=-6\) (x - coefficient is \(3\))
2. \(y - x=-5\) (x - coefficient is \(- 1\))

Step2: Determine multiplier

To eliminate x - terms, we want the coefficients of x to be equal in magnitude (so they can cancel when added or subtracted). The coefficient of x in the second equation is \(-1\). If we multiply the second equation by \(3\), the x - coefficient becomes \(3\times(-1)=-3\). Now, the x - coefficient in the first equation is \(3\) and in the second (after multiplication) is \(-3\). When we add the two equations, the x - terms (\(3x\) and \(-3x\)) will cancel.

Answer:

To eliminate the \(x\) - terms, multiply the equation \(y - x=-5\) by \(3\) on both sides.