Question

1. -5x + y = -3

3x - 8y = 24

Explanation:

Step1: Solve first equation for y

From \(-5x + y = -3\), we add \(5x\) to both sides:
\(y = 5x - 3\)

Step2: Substitute y into second equation

Substitute \(y = 5x - 3\) into \(3x - 8y = 24\):
\(3x - 8(5x - 3) = 24\)

Step3: Simplify and solve for x

Expand: \(3x - 40x + 24 = 24\)
Combine like terms: \(-37x + 24 = 24\)
Subtract 24: \(-37x = 0\)
Divide by \(-37\): \(x = 0\)

Step4: Substitute x back to find y

Substitute \(x = 0\) into \(y = 5x - 3\):
\(y = 5(0) - 3 = -3\)

Answer:

The solution to the system is \(x = 0\), \(y = -3\)