If 3x + 3y = 7 and 8x + 7y = 12 what is the average of x and y?

Explanation

3x+3y=7

3(x+y)=7

x+y=7/3

x+y=3.4(approx)

x=3.4-y......1)

8x+7y=12

8(3.4-y)+7y=12

27.2-8y+7y=12

-y=12-27.2

-y= -15.2

y=15.2

1)x=3.4-y

x=3.4-15.2

x= - 11.8

To find the average of x and y, we first need to find the values of x and y that satisfy the given equations. Let's solve the system of equations: 1. Multiply the first equation by 7 and the second equation by 3 to eliminate the y term: - 21x - 21y = 49 - 24x + 21y = 36 2. Add the two equations together: - 21x - 21y + 24x + 21y = 49 + 36 - 3x = 85 - x = 85/3 3. Substitute the value of x back into either of the original equations. Let's use the first equation: 3(85/3) + 3y = 7 85 + 3y = 7 3y = -78 y = -78/3 y = -26 So the solution to the system of equations is x = 85/3 and y = -26. To find the average of x and y, we add them together and divide by 2: Average = (x + y) / 2 = (85/3 - 26) / 2 = (85/3 - 78/3) / 2 = 7/3 / 2 = 7/6 Therefore, the average of x and y is 7/6 or 1.16

ND5-07-2023

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