Question

Question #1622e

Answer 1

`x = 7` and `y = 6`

If you like point form, it is: `(7,6)`

Explanation:

Given:

`2x+y=20" [1]"`
`6x-5y=12" [2]"`

We can use equation [1] to write y in terms of x by subtracting 2x from both sides:

`y=20-2x" [1.1]"`
`6x-5y=12" [2]"`

Substitute the right side of equation [1.1] for y in equation [2]:

`6x-5(20-2x)=12" [2.1]"`

Solve for the value of x:

`6x-100+10x=12" [2.1]"`

`16x = 112`

`x = 7`

We can use either equation [1] or [2] to find the corresponding value of y; I shall use equation [1]:

`2(7)+y = 20`

`y = 6`

Verify that the point `(7,6)` satisfies both equations:

`2(7)+6=20`
`6(7)-5(6)=12`

`20 = 20`
`12=12`

Verified