Answer:
I think its at 8%
Step-by-step explanation:
Answer:
The solution to the equation system given is:
- <u>x = 2</u>
- <u>y = -1</u>
Step-by-step explanation:
First, we must know the equations given:
- 2x + 3y = 1
- 3x + y = 5
Following Crammer's Rule, we have the matrix form:
![\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
Now we solve using the determinants:
![x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%281%2A1%29-%285%2A3%29%7D%7B%282%2A1%29-%283%2A3%29%7D%20%3D%20%5Cfrac%7B1-15%7D%7B2-9%7D%20%3D%5Cfrac%7B-14%7D%7B-7%7D%20%3D%202)
![y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%5C%5C3%265%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%282%2A5%29-%283%2A1%29%7D%7B%282%2A1%29-%283%2A3%29%7D%3D%5Cfrac%7B10-3%7D%7B2-9%7D%20%3D%5Cfrac%7B7%7D%7B-7%7D%3D-1)
Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:
- 2x + 3y = 1
- 2(2) + 3(-1)= 1
- 4 - 3 = 1
- 1 = 1
And, with the second equation:
- 3x + y = 5
- 3(2) + (-1) = 5
- 6 - 1 = 5
- 5 = 5
Answer:
Given the equation: ![3x^2+14x+16=0](https://tex.z-dn.net/?f=3x%5E2%2B14x%2B16%3D0)
The general equation of quadratic formula for
where a, b and c are constant;
then, the solution for this equation is given by;
......[1]
From the equation,
we have
a =2, b=14 and c=16
Substitute these values in [1] to solve for x;
or
![x=\frac{-14\pm\sqrt{196-192}}{6} =\frac{-14\pm\sqrt{4}}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-14%5Cpm%5Csqrt%7B196-192%7D%7D%7B6%7D%20%3D%5Cfrac%7B-14%5Cpm%5Csqrt%7B4%7D%7D%7B6%7D)
Simplify:
![x=\frac{-14\pm\sqrt{4}}{6} =\frac{-14\pm 2}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-14%5Cpm%5Csqrt%7B4%7D%7D%7B6%7D%20%3D%5Cfrac%7B-14%5Cpm%202%7D%7B6%7D)
then,
and
![x=\frac{-14-2}{6} =\frac{-16}{6} =\frac{-8}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-14-2%7D%7B6%7D%20%3D%5Cfrac%7B-16%7D%7B6%7D%20%3D%5Cfrac%7B-8%7D%7B3%7D)
Therefore, the solutions for the given equation is; x =-2 and ![x =-\frac{8}{3}](https://tex.z-dn.net/?f=x%20%3D-%5Cfrac%7B8%7D%7B3%7D)
Hey there,
The following attachment would be the graph.
Hope this helps you!