Solve the system of equations using the subtraction method.

6x + 5y = 82
2x + 5y = 54

x = 7 and y = 8

Step-by-step explanation: The pair of simultaneous equations given shall be solved by one of three known methods which are graphical method, substitution method and elimination method. When all of the unknown variables have a coefficient greater than 1, we shall use the elimination method which applies in this particular question.

6x + 5y = 82 ———(1)

2x + 5y = 54 ———(2)

Since the y variable has the same coefficient in both equations, we shall eliminate it by subtracting one equation from the other. Subtract equation (2) from equation (1) and we now have

4x = 28

Divide both sides of the equation by 4

x = 7

Having calculated x, substitute for the value of x into equation (1)

6x + 5y = 82

6(7) + 5y = 82

42 + 5y = 82

Subtract 42 from both sides of the equation

5y = 40

Divide both sides of the equation by 5

y = 8

Therefore x = 7 and y = 8

The solution is (19/2, 7)

Step-by-step explanation:

6x + 5y = 82

2x + 5y = 54

Multiply the second equation by -1, obtaining the equivalent system

6x + 5y = 82

-2x - 5y = -54

Combining these two equations eliminates the variable y temporarily:

4x = 28.  Thus, x = 7.  

To find y, substitute 7 for x in the second equation, obtaining 2x + 5(7) = 54.

Then 2x + 35 = 54, and 2x = 19.  Then x must be 19/2.

The solution is (19/2, 7)

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step-by-step explanation: