Question

add the equations to eliminate the x-terms.
4y + 3x = -6
3y - 3x = -15
? = ?

Explanation:

Step1: Multiply the second equation by 3

We have the second equation \( y - x = -5 \). Multiply each term by 3: \( 3(y - x)=3\times(-5) \), which simplifies to \( 3y - 3x = -15 \).

Step2: Add the two equations

The first equation is \( 4y + 3x = -6 \) and the modified second equation is \( 3y - 3x = -15 \). Add the left - hand sides and the right - hand sides separately:
\((4y + 3x)+(3y - 3x)=-6+(-15)\)
Simplify the left - hand side: \(4y+3x + 3y-3x=(4y + 3y)+(3x-3x)=7y\)
Simplify the right - hand side: \(-6-15=-21\)
So we get \(7y=-21\)

Answer:

\(7y=-21\) (If we want to solve for \(y\), we can divide both sides by 7: \(y = - 3\), but based on the addition of the equations to eliminate \(x\) - terms, the result of adding \(4y + 3x=-6\) and \(3y - 3x=-15\) is \(7y=-21\))