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:
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:
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- (8x - y) * 6 = 12 * 6
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- 48x - 6y = 72
Next, we subtract the second equation from the modified first equation:
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- 48x - 6y - (2x - 6y) = 72 - 3
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- 46x = 69
Divide both sides by 46 to solve for x:
Substitute x = 1.5 into the original first equation to solve for y:
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- 8(1.5) - y = 12
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- 12 - y = 12
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- -y = 0
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- 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.