Option a:
is the solution to the system of equations.
Explanation:
The equations are
and ![y=5 x+1](https://tex.z-dn.net/?f=y%3D5%20x%2B1)
Equating these two equations, we have,
![-\frac{2}{5} x-2=5 x+1](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B5%7D%20x-2%3D5%20x%2B1)
Taking LCM and multiplying both sides by 5, we get,
![-2 x-10=25 x+5](https://tex.z-dn.net/?f=-2%20x-10%3D25%20x%2B5)
Simplifying , we get,
![\begin{aligned}-10-5 &=25 x+2 \\-15 &=27 x \\-\frac{15}{27} &=x \\-\frac{5}{9} &=x\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-10-5%20%26%3D25%20x%2B2%20%5C%5C-15%20%26%3D27%20x%20%5C%5C-%5Cfrac%7B15%7D%7B27%7D%20%26%3Dx%20%5C%5C-%5Cfrac%7B5%7D%7B9%7D%20%20%26%3Dx%5Cend%7Baligned%7D)
Substituting the value of x in
, we get,
![\begin{aligned}&y=5\left(-\frac{5}{9}\right)+1\\&y=-\frac{25}{9}+1\\&y=-\frac{16}{9}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26y%3D5%5Cleft%28-%5Cfrac%7B5%7D%7B9%7D%5Cright%29%2B1%5C%5C%26y%3D-%5Cfrac%7B25%7D%7B9%7D%2B1%5C%5C%26y%3D-%5Cfrac%7B16%7D%7B9%7D%5Cend%7Baligned%7D)
Thus, the solution is ![\left(-\frac{5}{9},-\frac{16}{9}\right)](https://tex.z-dn.net/?f=%5Cleft%28-%5Cfrac%7B5%7D%7B9%7D%2C-%5Cfrac%7B16%7D%7B9%7D%5Cright%29)
Changing the solution from fraction to decimal, we get, ![(-0.556,-1.778)](https://tex.z-dn.net/?f=%28-0.556%2C-1.778%29)
Thus, the solution is ![(-0.5,-1.75)](https://tex.z-dn.net/?f=%28-0.5%2C-1.75%29)
Hence, option a is the correct answer.
A suitable calculator finds the determinant to be ...
... B. -203
_____
This can be calculated by hand by copying the first two columns to the right of the given matrix, then forming the sum of products of the downward diagonals and subtracting the sum of products of the upward diagonals.
... (-4)(3)(-5) +(-4)(-5)(-5) +(-3)(3)(2) -(-5)(3)(-3) -(2)(-5)(-4) -(-5)(3)(-4)
... = 60 -100 -18 -45 -40 -60
... = -203
The solution is 2610.
435
-06
——-
2610