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Solve the following system using the Elimination Method; 6x+y=10 and 2x+y=12.
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Solve the following system using the Elimination Method; 6x+y=10 and 2x+y=12.
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Mathematics
3 years
2021-08-20T00:16:48+00:00
2021-08-20T00:16:48+00:00 2 Answers
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Hey there!
The solution to the system is![Rendered by QuickLaTeX.com (\frac{1}{2}, 13)](https://documen.tv/wp-content/ql-cache/quicklatex.com-e476182c4f5efc4cb793496b4e9e6a53_l3.png)
To solve the system, we can multiply the second equation by -1:
Then, we add the two equations together, and solve for x:
Now, we plug the x value into one of the equations, and solve for y:
Now we know that the solution to the system is![Rendered by QuickLaTeX.com (\frac{1}{2}, 13)](https://documen.tv/wp-content/ql-cache/quicklatex.com-e476182c4f5efc4cb793496b4e9e6a53_l3.png)
Hope it helps and have an amazing day!
Answer:
(-1/2, 13)
Step-by-step explanation:
Multiply the 2nd equation by -1, obtaining the following system:
6x + y = 10
-2x – y = -12
——————
Combine like terms, obtaining:
6x + y = 10
-2x – y = -12
——————
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)