Question

Application Problem: What would be following system of equations? (2)/(3)x-(1)/(6)y=(1)/(2) 2x-4y=3

Answer 1

The system of equations is \((2/3)x - (1/6)y = (1/2)\) and \(2x - 4y = 3\). To solve this system, first convert the first equation to \(4x - y = 3\) by multiplying by 6, then use elimination or another method to find the solution.

Step-by-step explanation:

The system of equations provided by the student is:

1. 
   
3. \((2/3)x - (1/6)y = (1/2)\)
4. 
   
6. \(2x - 4y = 3\)

Let's solve this system step-by-step:

1. 
   
3. First, we can multiply the first equation by 6 to eliminate the fractions: \(4x - y = 3\).
4. 
   
6. Then, let's align this equation with the second equation:
7. 
   

• 
  
• \(4x - y = 3\)
• 
  
• \(2x - 4y = 3\)
• 
  

We now have a system of linear equations that can be solved using methods like substitution, elimination, or graphing.

In this problem, perhaps the simplest method to proceed with is elimination. By multiplying the second equation by 2, it can be aligned with the first equation in terms of the coefficient of x, and then subtracted to solve for y.