Question

here is a system of equations:
y = -3x - 5
y = 4x + 30
how many solutions does this system have?
no solution one solution infinitely many solutions
what is the solution?

Explanation:

Step1: Set the equations equal

Since both equal \( y \), set \( -3x - 5 = 4x + 30 \).

Step2: Solve for \( x \)

Add \( 3x \) to both sides: \( -5 = 7x + 30 \).
Subtract 30: \( -35 = 7x \).
Divide by 7: \( x = -5 \).

Step3: Find \( y \)

Substitute \( x = -5 \) into \( y = -3x - 5 \):
\( y = -3(-5) - 5 = 15 - 5 = 10 \).

Answer:

The system has one solution, and the solution is \( x = -5 \), \( y = 10 \) (or as an ordered pair \((-5, 10)\)).