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olga_2 [115]
3 years ago
6

Systems of Linear Equations What are the different ways to solve a system of linear equations? When do you get an answer to a sy

stem of linear equations that has one solution, no solution and infinitely many solutions? Solve each of the following systems by graphing. y = -x – 7 y = 4/3 x – 7 y = -3x – 5 y = x + 3 y = -2x + 5 y = 1/3 x – 2 3x + 2y = 2 x + 2y = -2 x + 3y = -9 2x – y = -4 x – 2y = 2 -x + 4y = -8 5x + y = -2 x + y = 2

Mathematics
2 answers:
Mrac [35]3 years ago
3 0

Answer:

Different ways to solve a system of linear equations:

  • isolate one variable in one equation and replace it in the other equation
  • multiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remains
  • graph the equation and look at the intersection point

If you graph the system:

  • there is only one solution if the lines intersects at only one point
  • there is no solution if the lines don't intersect each other (they are parallel)
  • there are infinitely many solutions if the lines overlap each other (they are the same equation multiplied by some constant)

Step-by-step explanation:

1st system

y = -x – 7  

y = 4/3 x – 7  

solution: x= 0, y = 7

2nd system

y = -3x – 5  

y = x + 3  

solution: x = -2, y = 1

3rd system

y = -2x + 5  

y = 1/3 x – 2

solution:  x = 3, y = -1

4th system

3x + 2y = 2  

x + 2y = -2  

solution: x = 2, y = -2

5th system

x + 3y = -9  

2x – y = -4

solution:  x = -3, y = -2

6th system

x – 2y = 2

-x + 4y = -8

solution:  x = -4, y = -3

7th system

5x + y = -2  

x + y = 2

solution: x = -1, y = -3

nignag [31]3 years ago
3 0

75% I think x = -1, y = -3

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krok68 [10]

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30 hours

Step-by-step explanation:

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7 0
2 years ago
107 = 7 - 2(7b - 1) what does b equal?
topjm [15]

107 = 7 -2 (7b - 1)

First, distribute -2 to all terms within the parenthesis

-2(7b - 1) = -14b + 2

107 = 7 -14b + 2

Combine like terms

107 = -14b (+7 + 2)

107 = -14b + 9

Isolate the b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

Subtract 9 from both sides

107 (-9) = -14b + 9 (-9)

107 - 9 = -14b

98 = -14b

Isolate the b. Divide -14 from both sides

(98)/-14 = (-14b)/-14

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hope this helps

5 0
3 years ago
Find the value of x for which f(x)=-2
enyata [817]

Answer:

x=2

Step-by-step explanation:

6 0
3 years ago
Asap! please help i’ll give brainliest
Alex777 [14]

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6 0
3 years ago
Hi, the answer is K but can anyone show why
dlinn [17]

Let's do 51 and 52.

51. The contrapositive has the same truth value as the original statement. That's opposed to the converse, which may or may not be true independent of the original statement.

The contrapositive of IF P THEN Q is IF not Q THEN not P.  They're equivalent.  Here that's If the cat is not female then it is not tricolor.

Answer: C

52.  

(x^3)^{(4-b^2)}=1

x^{3(4-b^2)} = 1

For the statement to be true, the exponent must be zero:

3(4-b^2) = 0

b^2 = 4

b = \pm 2

Both positive 2 and negative 2 have a square of 4.

Answer: K

By the way, usually we assume 0^0=1 so the restriction that x \ne 0 isn't really necessary.  Think of the definition of a polynomial or the binomial expansion:

\displaystyle f(x)=\sum_{k=0}^n a_k x^k

\displaystyle(x+y)^n=\sum_{k=0}^n {n \choose k} x^{k}y^{n-k}

For these common equalities to work when x=0 we need to define 0^0=1


3 0
3 years ago
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