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Sagot :
Answer is b. (-1, -5)
Step by step
Substitute the x and y values into both equations to find equality
Answer b. Makes both equations equal
2x + y = -7
2(-1) + (-5) = -7
-2 -5 = -7
-7 = -7
It equals now let’s do the 2nd one
x - y = 4
-1 -(-5) = 4
4 = 4
This one equals too. I did the math on the other three answers and they did not equal.
Problem solved!
Step by step
Substitute the x and y values into both equations to find equality
Answer b. Makes both equations equal
2x + y = -7
2(-1) + (-5) = -7
-2 -5 = -7
-7 = -7
It equals now let’s do the 2nd one
x - y = 4
-1 -(-5) = 4
4 = 4
This one equals too. I did the math on the other three answers and they did not equal.
Problem solved!
Answer: B. (-1, -5)
Step-by-step explanation:
Given equations
2x + y = -7
x - y = 4
Concept
[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
[tex]A*A^{-1}=A^{-1}*A=I~(Which~is~basically~1)[/tex]
Convert into matrix
[tex]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]
Calculate the inverse of the matrix
[tex]A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right][/tex]
[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
[tex]A^{-1}=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right][/tex]
Solve by multiplying the inverse of the matrix
[tex]A*A^{-1}=A^{-1}*A=I[/tex]
[tex]-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]
[tex]1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3}\left[\begin{array}{ccc}3\\15\\\end{array}\right][/tex]
Simplify by multiplication
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right][/tex]
Therefore, the answer is [tex]\Large\boxed{(-1,~-5)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
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