Answer:
Given equation are:
......[1]
.....[2]
- The two lines are parallel lines then their slopes will be equal.
- When two lines are perpendicular then, the slope of lines are the negative reciprocals of each other.
Now, Equation of a line is in the form of y =mx+b where m is the slope of the line.
Slope
of equation of line in [1] is;
then;
Slope
of equation of line in [2];
Add both sides 2x we get;
-2x + 8y + 2x = 2x + 4
Simplify:
8y = 2x +4
Divide both sides by 8 we get;
then;
Therefore, the given two lines are neither parallel nor perpendicular.
Answer:
The solutions for the given system of equations are:
Step-by-step explanation:
Given the equation system:
We obtain the following matrix:
![\left[\begin{array}{cccc}3&1&4&-3\\-1&1&4&17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%261%264%26-3%5C%5C-1%261%264%2617%5Cend%7Barray%7D%5Cright%5D)
<u>Step 1:</u> Multiply the fisrt row by 1/3.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\-1&1&4&17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C-1%261%264%2617%5Cend%7Barray%7D%5Cright%5D)
<u>Step 2:</u> Sum the first row and the second row.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&\frac{4}{3} &\frac{16}{3}&16\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C0%26%5Cfrac%7B4%7D%7B3%7D%20%26%5Cfrac%7B16%7D%7B3%7D%2616%5Cend%7Barray%7D%5Cright%5D)
<u>Step 3:</u> Multiply the second row by 3/4.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&1 &4&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C0%261%20%264%2612%5Cend%7Barray%7D%5Cright%5D)
<u>Step 4:</u> Multiply the second row by -1/3 and sum the the first row.
![\left[\begin{array}{cccc}1&0 &0&-5\\0&1 &4&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%20%260%26-5%5C%5C0%261%20%264%2612%5Cend%7Barray%7D%5Cright%5D)
The result of the reduced matrix is:
This is equal to:
These are the solutions for the system of equations in terms of z, where z can be any number.
Endbdbr rvrbbfbfbrbrbfbfbfdbdbdbdbdbdbebdbdbdbdbddjsjsejnebebebeebdbdbdbdbdbdbdbdbdbdbsbsbsbdbbssbsbsb
The answer is 270 because 2,565/9.5=270 hope this helps!
145%
200/200: 100%
90/200= 45%
