Use the elimination method to solve the system of equations. 3x + 4y = 8
x-y=12
O A. (8,4)
O B. (-4,8)
C. (0,2)
O D. (8,-4)

Option D. (8, – 4)

Step-by-step explanation:

3x + 4y = 8 (1)

x – y = 12 (2)

To solve the above equation by elimination method, do the following:

Step 1:

Multiply equation 1 by the coefficient of x in equation 2 i.e 1.

Multiply equation 2 by the coefficient of x in equation 1 i.e 3. This is illustrated below:

1 × Equation 1

1 × (3x + 4y = 8)

3x + 4y = 8 (3)

3 × Equation 2

3 × ( x – y = 12)

3x – 3y = 36(4)

Step 2:

Subtract equation 3 from equation 4. This is illustrated below:

. 3x – 3y = 36

– (3x + 4y = 8)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

– 7y = 28

Divide both side by the coefficient of y i.e –7

y = 28/–7

y = – 4

Step 3:

Substitute the value of y into any of the equation to obtain the value of x. In this case, we shall substitute the value of y into equation 2 as shown below:

x – y = 12

y = –4

x – (–4) = 12

x + 4 = 12

x = 12 – 4

x = 8

Therefore, the solution to the equation above is (8, – 4)

h

step-by-step explanation:

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