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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?

User Sujee
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1 Answer

7 votes

Final answer:

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.

User Vicport
by
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