Question 1185998
Here's how to solve this system of linear equations for x and y:

**Method 1: Substitution**

1. **Solve one equation for one variable:**  It's easiest to solve the second equation for y:
   43y = 303 - 338x
   y = (303 - 338x) / 43

2. **Substitute:** Substitute this expression for y into the first equation:
   126x + 198 * (303 - 338x) / 43 = 150

3. **Simplify and solve for x:**
   126x + (60000 - 66924x)/43 = 150
   5418x + 60000 - 66924x = 6450
   -61506x = -53550
   x = 53550 / 61506
   x ≈ 0.872

4. **Substitute x back to find y:** Substitute the value of x into either original equation.  Using the first equation is simplest.
   126 * 0.872 + 198y = 150
   110 + 198y = 150
   198y = 40
   y = 40 / 198
   y ≈ 0.202

**Method 2: Elimination**

1. **Multiply equations to match coefficients:** We'll eliminate y. Multiply the first equation by 43 and the second equation by 198:
   (126x + 198y = 150) * 43  =>  5418x + 8514y = 6450
   (338x + 43y = 303) * 198  =>  66924x + 8514y = 60054

2. **Subtract the equations:** Subtract the first new equation from the second:
   61506x = 53604

3. **Solve for x:**
   x = 53604 / 61506
   x ≈ 0.872

4. **Substitute x back to find y:** Substitute the value of x into either original equation.
   126 * 0.872 + 198y = 150
   y ≈ 0.202

**Solution:**

x ≈ 0.872
y ≈ 0.202