Question

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

Answer 1

Answer:

The solution is: (2, -1)

Step-by-step 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)

Answer 2

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:

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