Question

Solve the system.
2x+y = 3
-2y = 14 - 6x

Answer 1

For this case we have the following system of equations:

`2x + y = 3\\-2y = 14-6x`

We clear "y" from the second equation:

`y = \frac {14} {- 2} - \frac {6x} {- 2}\\y = -7 + 3x`

We substitute in the first equation:

`2x + (- 7 + 3x) = 3\\2x-7 + 3x = 3\\5x-7 = 3\\5x = 3 + 7\\5x = 10\\x = \frac {10} {5}\\x = 2`

So:

`y = -7 + 3x\\y = -7 + 3 (2)\\y = -7 + 6\\y = -1`

The solution is:
`(x, y) :( 2, -1)`

Answer:

`(x, y) :( 2, -1)`

Answer 2

The solution is: (2, -1)

Explanation:

First we rewrite the second system equation

`-2y = 14 - 6x` →
`6x-2y=14`

Now we have the following system of equations:

`2x+y = 3`

`6x-2y=14`

To solve the system multiply the first equation by -3 and add it to the second equation

`-6x+-3y = -9`

`6x-2y=14`

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`0-5y=5`

`y=-1`

Now we substitute the value of y in the first equation and solve for x

`2x-1 = 3`

`2x= 4`

`x= 2`

The solution is: (2, -1)