Question

Solve the following system using the Elimination Method; 6x+y=10 and 2x+y=12.

Answer 1

Hey there!

The solution to the system is $(\frac{1}{2}, 13)$

To solve the system, we can multiply the second equation by -1:

$-2x - y = -12$

Then, we add the two equations together, and solve for x:

$4x = -2$

$x = \frac{-1}{2}$

Now, we plug the x value into one of the equations, and solve for y:

$2(\frac{1}{2} ) + y = 12$

$-2 + y = 12$

$y = 13$

Now we know that the solution to the system is $(\frac{1}{2}, 13)$

Hope it helps and have an amazing day!

Answer 2

Answer:

(-1/2, 13)

Step-by-step explanation:

Multiply the 2nd equation by -1, obtaining the following system:

6x + y = 10

-2x  - y = -12

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Combine like terms, obtaining:

6x + y = 10

-2x  - y = -12

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4x     = -2

Dividing both sides by 4 yields x = -2/4, or x = -1/2

Substituting -1/2 for x in the second equation yields:

2(-1/2) + y = 12, or

-1 + y = 12.  Then y = 13, and the solution is

(-1/2, 13)