The solution is solved using Equalization methods. Hence the answer to A is such that y= -2 and x = 12
What is the Equalization method?
The Equalization method refers to a method whereby a quantity that is unknown in two equations is isolated and equated.
The solution to equation one is thus given below:
[tex]\{ \mathrm{}_{x + 3y = 6}^{2x + 5y = 16}[/tex]
Step I - Isolate any two variables.
In this case, we will isolate x. Hence we will have:
2x + 5y = 16 → x = (16 - 5y)/2 .............................1
x + 3y = 6 → x = (7 - 3y) .............................2
From 1 and 2 above, we can see that both equations are now equal to x, Using the principle of transitivity, we can state that:
Since both formulas are now equal to x, therefore:
(16 - 5y)/2 = (7 - 3y)...............................3
Simplifying and collecting like terms from 3 above, we now have:
(16 - 5y) = 2(7 - 3y)
that is 16 - 5y = 14-6y
This will give us:
6y-5y= 14-16
y = -2
Step II - Substitute Y into any of the original equations to get x.
Recall that we have x + 3y = 6
Therefore, x = 6-3y
That is x = 6-3(-2)
x = 6 + 6 = 12
Hence, for Equation A, x = 12; y = -2
Equation B:
Using the same method, we arrive at: x =45; and y = -3
Equation C:
Using the same method, we arrive at: x = 2; and y = 0
Learn more about Equalization Method at:
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