Question

Solve the system of equations. 2x + 3y = 6 x + y = 4 (6, -2) (-2, 6) (-3, 4) (0, 2)

Answer 1

(6,-2)

Explanation:

Given equations are
`2x + 3y = 6` and
`x + y = 4`.

Solve 2nd equation
`x + y = 4` for y

`x + y = 4`

`y = 4-x` ...(i)

Plug value of y from equation (i) into first equation
`2x + 3y = 6`

`2x + 3(4-x) = 6`

`2x + 12-3x = 6`

`12-x = 6`

`-x = 6-12`

`-x = -6`

`x = 6`

Plug x=6 into equation (i)

`y = 4-x`

`y = 4-6`

`y = -2`

Hence final answer is x=6, y=-2 or we can write that in (x,y) form as (6,-2)

Answer 2

(6,-2)

Explanation:

2x + 3y = 6

x + y = 4

Multiply the second equation by -2 to eliminate x

-2(x+y) = -2*4

-2x-2y = -8

Add this to the first equation

2x + 3y = 6

-2x -2y = -8

---------------------

y = -2

Now we need to find x

x+y = 4

x-2 = 4

Add 2 to each side

x-2+2 = 4+2

x = 6

(6,-2)