Question 1173100
Let's break down this problem and set up the system of linear inequalities.

**Variables**

* Let 'x' represent the amount of savings in the bank with 4% interest.
* Let 'y' represent the amount of savings in the bank with 6% interest.

**Inequalities**

1.  **Combined Savings:**
    * The combined amount of savings is at least Php 150,000.
    * Equation: x + y ≥ 150,000

2.  **Interest Earned:**
    * The total interest earned is at most Php 12,000.
    * Interest from 4% bank: 0.04x
    * Interest from 6% bank: 0.06y
    * Equation: 0.04x + 0.06y ≤ 12,000

3.  **Non-negative Savings:**
    * Savings cannot be negative.
    * Equations: x ≥ 0 and y ≥ 0

**System of Linear Inequalities**

* x + y ≥ 150,000
* 0.04x + 0.06y ≤ 12,000
* x ≥ 0
* y ≥ 0

**Graphing the Inequalities**

1.  **x + y ≥ 150,000**

    * To graph this, first graph the line x + y = 150,000.
    * Find the intercepts:
        * If x = 0, y = 150,000
        * If y = 0, x = 150,000
    * Draw the line connecting (150000,0) and (0,150000). Since the inequality is "greater than or equal to," use a solid line.
    * Shade the region above the line, as that represents x + y ≥ 150,000.

2.  **0.04x + 0.06y ≤ 12,000**

    * To graph this, first graph the line 0.04x + 0.06y = 12,000.
    * To make it easier to graph, we can multiply the entire equation by 100
        * 4x+6y=1200000
    * Then we can divide the entire equation by 2
        * 2x+3y=600000
    * Find the intercepts:
        * If x = 0, 3y = 600000, y = 200,000
        * If y = 0, 2x = 600000, x = 300,000
    * Draw the line connecting (300000, 0) and (0, 200000). Since the inequality is "less than or equal to," use a solid line.
    * Shade the region below the line, as that represents 0.04x + 0.06y ≤ 12,000.

3.  **x ≥ 0 and y ≥ 0**

    * These inequalities restrict the solution to the first quadrant (where both x and y are non-negative).

**Finding the Solution Region**

* The solution region is the area where all shaded regions overlap in the first quadrant.
* The corner points of this region are important for finding specific solutions.

**Corner Points**

* Intersection of x + y = 150,000 and x = 0: (0, 150,000)
* Intersection of x + y = 150,000 and 0.04x + 0.06y = 12,000:
    * Solve the system of equations.
    * From x + y = 150,000, y = 150,000 - x.
    * Substitute into 0.04x + 0.06(150,000 - x) = 12,000
    * 0.04x + 9,000 - 0.06x = 12,000
    * -0.02x = 3,000
    * x = -150000. There is an error.
    * multiply 0.04x + 0.06y = 12000 by 100. 4x+6y=1200000, then divide by 2. 2x+3y=600000
    * multiply x+y=150000 by 2. 2x+2y=300000. Substract that from 2x+3y=600000. y=300000. x=-150000. There is still an error.
    * Multiply x+y=150000 by 0.04. 0.04x+0.04y=6000.
    * Subtract that from 0.04x+0.06y=12000. 0.02y=6000. y=300000. x=150000-300000. x=-150000. There is still an error.
    * 0.04x + 0.06(150000-x)=12000
    * 0.04x +9000-0.06x=12000
    * -0.02x=3000
    * x=-150000
    * There is an error with the problem itself. The intersection of those two lines is outside of the first quadrant.

* Intersection of 0.04x + 0.06y = 12,000 and y = 0: (300,000, 0)
* Intersection of x=0 and y=0 (0,0)

The solution region is the area between the lines, and within the first quadrant.