Question

1. $-5x + 5y = -5$ $10x - 4y = -14$

Explanation:

Step1: Simplify the first equation

Divide the first equation \(-5x + 5y = -5\) by \(-5\) to simplify it.
\(\frac{-5x}{-5}+\frac{5y}{-5}=\frac{-5}{-5}\)
Which simplifies to \(x - y = 1\), and we can rewrite it as \(x = y + 1\).

Step2: Substitute \(x\) into the second equation

Substitute \(x = y + 1\) into the second equation \(10x - 4y = -14\).
\(10(y + 1)-4y=-14\)
Expand the left - hand side: \(10y+10 - 4y=-14\)
Combine like terms: \(6y+10=-14\)

Step3: Solve for \(y\)

Subtract 10 from both sides of the equation \(6y + 10=-14\):
\(6y=-14 - 10\)
\(6y=-24\)
Divide both sides by 6: \(y=\frac{-24}{6}=-4\)

Step4: Solve for \(x\)

Substitute \(y = - 4\) into \(x = y + 1\):
\(x=-4 + 1=-3\)

Answer:

The solution to the system of equations is \(x=-3\) and \(y = - 4\)