Question

8x−y=12 2x−6y=3 . Consider the system of equations above. If (x,y) is the solution to the system, then what is the value of x+y?

Answer 1

To find the value of x + y for the given system of equations, we solved the system using the elimination method to get x = 1.5 and y = 0, resulting in x + y = 1.5.

Step-by-step explanation:

The system of linear equations given is:

• 
  
• 8x - y = 12
• 
  
• 2x - 6y = 3

We want to find the value of x + y. To do this, we can solve the system using either substitution or elimination methods. Let's use the elimination method.

Multiply the first equation by 6 to make the coefficients of y's the same:

• 
  
• (8x - y) * 6 = 12 * 6
• 
  
• 48x - 6y = 72

Next, we subtract the second equation from the modified first equation:

• 
  
• 48x - 6y - (2x - 6y) = 72 - 3
• 
  
• 46x = 69

Divide both sides by 46 to solve for x:

• 
  
• x = 69 / 46
• 
  
• x = 1.5

Substitute x = 1.5 into the original first equation to solve for y:

• 
  
• 8(1.5) - y = 12
• 
  
• 12 - y = 12
• 
  
• -y = 0
• 
  
• y = 0

Now we can add x and y to find their sum:

x + y = 1.5 + 0 = 1.5

Therefore, the value of x + y is 1.5.