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adell [148]
3 years ago
9

Solve the system by the substitution method. x + y = 2 y= x2 - 6x + 8

Mathematics
1 answer:
ruslelena [56]3 years ago
8 0

Answer:

The solution of the given system is (2,0)

Step-by-step explanation:

Here, the given system of equations is:

x + y = 2    .............. (1)

y= x^2 - 6x +  8  ........  (2)

Now from (1) x = 2 - y

Substitute this value of x = 2- y in (2) ,we get:

y= (2-y)^2 - 6(2-y) +  8\\\implies y = 4 + y^2 - 4y - 12 + 6y + 8\\or, y^2 + y  = 0\\\implies y(y +1) = 0

⇒  y = 0 or,  y = -1

Now, if y = 0, x  = 2

and if x= -1, y = 2-(-1)  = 2+1  = 3, or y = 3

But (x = -1 , y = 3 )is NOT  a solution of (2).

Hence, the solution of the given system is (2,0)

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gizmo_the_mogwai [7]

Use order of operations.

-23-20-(-17)+(-5)x(-2)+4x5

Do all multiplication steps.

-23-20-(-17)+10+20

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answer: 4

8 0
3 years ago
A large bowl contains 10 small balls and each ball has a color and a number. The 10 balls are denoted by B1, B2, B3, B4, R1, R2,
nasty-shy [4]

Answer:

Size of N(S) = 90, or S=90

Step-by-step explanation:

So since there are 10 items:

Each single item has 9 possibilities to be paired with, since it is drawn without replacement, and 1 item can't be drawn again.

So : 10 items x 9 possibilites = array of 90

SO ANSWER : 90

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4 0
3 years ago
Simplify 5+4x(8-6)^2<br> please help me please hurry please
Fed [463]
5+16x.......................
7 0
3 years ago
Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5​
Bond [772]

Answer:

The solution to the equation system given is:

  • <u>x = 2</u>
  • <u>y = -1</u>

Step-by-step explanation:

First, we must know the equations given:

  1. 2x + 3y = 1
  2. 3x + y = 5​

Following Crammer's Rule, we have the matrix form:

\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]

Now we solve using the determinants:

x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2

y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

  • 2x + 3y = 1
  • 2(2) + 3(-1)= 1
  • 4 - 3 = 1
  • 1 = 1

And, with the second equation:

  • 3x + y = 5​
  • 3(2) + (-1) = 5
  • 6 - 1 = 5
  • 5 = 5

 

4 0
2 years ago
P/4+=16<br> Pls show work!!
Dima020 [189]

Answer:

P = 64

Step-by-step explanation:

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3 0
3 years ago
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