Question

What is the solution of the system? Use the elimination method. 2x+y=20.  6x−5y=12 Enter your answer in the boxes.

Answer 1

The solution of the system of equations is (7,6). The value of x is 7 and the value of y is 6.

Explanation:

The given equations are

`2x+y=20` .... (1)

`6x-5y=12` .... (2)

Use elimination method to find the value of x and y.

Multiply equation (1) by 5.

`10x+5y=100` .... (3)

Now, add equation (2) and (3) to eliminate variable y.

`(6x+10x)=(100+12)`

`16x=112`

`x=(112)/(16)`

`x=7`

The value of x is 7. Substitute this value in equation (1).

`2(7)+y=20`

`14+y=20`

Subtract both sides by 14.

`y=20`

Therefore the solution of the system of equations is (7,6). The value of x is 7 and the value of y is 6.

Answer 2

Given

2x + y = 20 . . . (1)
6x - 5y = 12 . . . (2)

(1) x 3 ⇒ 6x + 3y = 60 . . . (3)

(2) - (3) ⇒ -8y = -48

⇒ y = -48 / -8 = 6

Substituting for y in (1), we have

2x + 6 = 20
2x = 20 - 6 = 14
x = 14 / 2 = 7.

Therefore, the solution to the system is

x = 7 and y = 6.