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Ainat [17]
4 years ago
7

Solve the system of equations. −9y+4x−20=0 ​−7y+16x−80=0 ​​

Mathematics
2 answers:
Kitty [74]4 years ago
4 0
Move −20-20 to the right side of the equation because it does not contain a variable.−9y+4x=20-9y+4x=20−7y+16x−80=0-7y+16x-80=0Move −80-80 to the right side of the equation because it does not contain a variable.−9y+4x=20-9y+4x=20−7y+16x=80-7y+16x=80Write the system of equations in matrix form.[4−92016−780][4-92016-780]Find the reduced row echelon form of the matrix.Tap for more steps...[105010][105010]Use the result matrix to declare the final solutions to the system of equations.x=5x=5y=0y=0The solution is the set of ordered pairs that makes the system true.(5,0)(5,0)Decompose a solution vector by re-arranging each equation represented in the row-reduced form of the augmented matrix by solving for the dependent variable in each row yields the vector equality.X=[xy]=[50]
Katarina [22]4 years ago
4 0
-9y + 4x - 20 = 0.....-9y + 4x = 20
-7y + 16x - 80 = 0....-7y + 16x = 80

-9y + 4x = 20.....multiply by -4
-7y + 16x = 80
----------------
36y - 16x = -80 (result of multiplying by -4)
-7y + 16x = 80
------------------add
29y = 0
y = 0

-9y + 4x = 20
-9(0) + 4x = 20
4x = 20
x = 20/4
x = 5

solution is (5,0) <==
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The difference of two numbers is 1. What is the smallest possible value for the sum of their squares?​
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X= 1 number
Y= a number that is 1 less than x
Y= x-1

The sum of squares=

X^2 + (x-1)^2 = x^2 + x^2 - 2x + 1
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Assuming that integers = numbers. We could try some values

When x = 0, the sum of squares = 1
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If you put this into a graph, it is a parabola and we see that the minimum value hits at x = 1/2.

To check this value:

2x^2 - 2x + 1 = 2·(1/4) - 2·(1/2) + 1
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When you look back at the question, it asks for 2 answers

X= 1/2
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What is the sum of their squares?

1/4 + 1/4 = 1/2

That fits with graph too.

Answers: 1/2 and -1/2

Hope this helps!!
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