Answer:
The system of equations has infinite solutions
Step-by-step explanation:
∵ y = -3x - 7 ⇒ (1)
∵ -6x - 2y = 14 ⇒ (2)
→ Substitute y in equation (2) by equation (1)
∴ -6x - 2(-3x - 7) = 14
→ Simplify the left side
∵ -6x - 2(-3x) - 2(-7) = 14
∴ -6x + 6x + 14 = 14
→ Add the like terms in the left side
∵ (-6x + 6x) + 14 = 14
∴ 0 + 14 = 14
∴ 14 = 14
∵ The variable is disappeared and the two sides of the equation equal
∴ The equation has many solutions
→ That means x and y can be any numbers
∴ The system of equations has infinite solutions
Answer:
the answer is B) 12a+6b
Step-by-step explanation:
3+9=12 so 3a+9a=12a,
7-1=6 so 7b-(1)b=6b
Answer:
x = 5, y = 4
Step-by-step explanation:
![\left\{\begin{array}{ccc}4x+5y=40\\x-y=1\end{array}\right\\\\A=\left[\begin{array}{ccc}4&5\\1&-1\end{array}\right]\\\\detA=\left|\begin{array}{ccc}4&5\\1&-1\end{array}\right|=(4)(-1)-(1)(5)=-4-5=-9\\\\A^D=\left[\begin{array}{ccc}-1&-1\\-5&4\end{array}\right]\\\\\left(A^D\right)^T=\left[\begin{array}{ccc}-1&-5\\-1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D4x%2B5y%3D40%5C%5Cx-y%3D1%5Cend%7Barray%7D%5Cright%5C%5C%5C%5CA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%265%5C%5C1%26-1%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CdetA%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D4%265%5C%5C1%26-1%5Cend%7Barray%7D%5Cright%7C%3D%284%29%28-1%29-%281%29%285%29%3D-4-5%3D-9%5C%5C%5C%5CA%5ED%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-1%5C%5C-5%264%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Cleft%28A%5ED%5Cright%29%5ET%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-5%5C%5C-1%264%5Cend%7Barray%7D%5Cright%5D)
![A^{-1}=\dfrac{1}{detA}\left(A^D\right)^T\\\\A^{-1}=\dfrac{1}{-9}\left[\begin{array}{ccc}-1&-5\\-1&4\end{array}\right]=\left[\begin{array}{ccc}\dfrac{1}{9}&\dfrac{5}{9}\\\dfrac{1}{9}&-\dfrac{4}{9}\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7BdetA%7D%5Cleft%28A%5ED%5Cright%29%5ET%5C%5C%5C%5CA%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7B-9%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-5%5C%5C-1%264%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cdfrac%7B1%7D%7B9%7D%26%5Cdfrac%7B5%7D%7B9%7D%5C%5C%5Cdfrac%7B1%7D%7B9%7D%26-%5Cdfrac%7B4%7D%7B9%7D%5Cend%7Barray%7D%5Cright%5D)
![A\cdot\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}40\\1\end{array}\right] \\\\A^{-1}A\cdot\left[\begin{array}{ccc}x\\y\end{array}\right] =A^{-1}\cdot\left[\begin{array}{ccc}40\\1\end{array}\right] \\\\\left[\begin{array}{ccc}x\\y\end{array}\right] =A^{-1}\cdot\left[\begin{array}{ccc}40\\1\end{array}\right]](https://tex.z-dn.net/?f=A%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D40%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5CA%5E%7B-1%7DA%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3DA%5E%7B-1%7D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D40%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3DA%5E%7B-1%7D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D40%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}\dfrac{1}{9}&\dfrac{5}{9}\\\dfrac{1}{9}&-\dfrac{4}{9}\end{array}\right]\cdot\left[\begin{array}{ccc}40\\1\end{array}\right] \\\\\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}\left(\frac{1}{9}\right)(40)+\left(\frac{5}{9}\right)(1)\\\\\left(\frac{1}{9}\right)(40)+\left(-\frac{4}{9}\right)(1)\end{array}\right]\\\\\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}5\\4\end{array}\right]\Rightarrow x=5,\ y=4](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cdfrac%7B1%7D%7B9%7D%26%5Cdfrac%7B5%7D%7B9%7D%5C%5C%5Cdfrac%7B1%7D%7B9%7D%26-%5Cdfrac%7B4%7D%7B9%7D%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D40%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cleft%28%5Cfrac%7B1%7D%7B9%7D%5Cright%29%2840%29%2B%5Cleft%28%5Cfrac%7B5%7D%7B9%7D%5Cright%29%281%29%5C%5C%5C%5C%5Cleft%28%5Cfrac%7B1%7D%7B9%7D%5Cright%29%2840%29%2B%5Cleft%28-%5Cfrac%7B4%7D%7B9%7D%5Cright%29%281%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%5C%5C4%5Cend%7Barray%7D%5Cright%5D%5CRightarrow%20x%3D5%2C%5C%20y%3D4)
Answer:
it is c
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