Question

1. $-3x + 3y = 3$

$-5x + y = 13$

Explanation:

Step1: Solve the second equation for y

From \(-5x + y = 13\), we can express \(y\) in terms of \(x\) by adding \(5x\) to both sides.
\(y = 5x + 13\)

Step2: Substitute y into the first equation

Substitute \(y = 5x + 13\) into \(-3x + 3y = 3\).
\(-3x + 3(5x + 13) = 3\)

Step3: Simplify and solve for x

First, distribute the 3 in \(3(5x + 13)\):
\(-3x + 15x + 39 = 3\)
Combine like terms:
\(12x + 39 = 3\)
Subtract 39 from both sides:
\(12x = 3 - 39\)
\(12x = -36\)
Divide both sides by 12:
\(x = \frac{-36}{12}\)
\(x = -3\)

Step4: Substitute x back to find y

Now that we have \(x = -3\), substitute it into \(y = 5x + 13\).
\(y = 5(-3) + 13\)
\(y = -15 + 13\)
\(y = -2\)

Answer:

The solution to the system of equations is \(x = -3\) and \(y = -2\)