Solve the system of equations: 6x + y + 16 = 0 4y - 3x + 10 = 0

Solution:

• Multiply the second equation by 2:
• \[ 2(4y - 3x + 10) = 2(0) \]
• \[ 8y - 6x + 20 = 0 \]
• Rearrange to align terms:
• \[ -6x + 8y + 20 = 0 \]
• Now we have the system:
• \[ 6x + y + 16 = 0 \]
• \[ -6x + 8y + 20 = 0 \]
• Add the two equations together to eliminate x:
• \[ (6x + y + 16) + (-6x + 8y + 20) = 0 + 0 \]
• \[ 9y + 36 = 0 \]
• Solve for y:
• \[ 9y = -36 \]
• \[ y = -4 \]
• Substitute the value of y back into the first equation (6x + y + 16 = 0) to solve for x:
• \[ 6x + (-4) + 16 = 0 \]
• \[ 6x + 12 = 0 \]
• \[ 6x = -12 \]
• \[ x = -2 \]

• \[ 4(-4) - 3(-2) + 10 = 0 \]
• \[ -16 + 6 + 10 = 0 \]
• \[ 0 = 0 \]
• The solution is correct.

Answer: x = -2, y = -4