Question

1. 30x + 50y - 100 = 0

3x - 15y - 30 = 0

Explanation:

Step1: Simplify the first equation

Divide \(30x + 50y - 100 = 0\) by 10: \(3x + 5y - 10 = 0\), then \(3x + 5y = 10\).

Step2: Simplify the second equation

Divide \(3x - 15y - 30 = 0\) by 3: \(x - 5y - 10 = 0\), then \(x - 5y = 10\).

Step3: Solve the system of equations

Add the two simplified equations: \((3x + 5y)+(x - 5y)=10 + 10\), \(4x = 20\), so \(x = 5\).
Substitute \(x = 5\) into \(x - 5y = 10\): \(5 - 5y = 10\), \(-5y = 5\), \(y = -1\).

Answer:

The solution of the system is \(x = 5\), \(y = -1\) (the intersection point is \((5, -1)\) on the coordinate plane).