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ipn [44]
3 years ago
5

−4x+7y+5= 0x−3y=−5​How many solutions does the system have?

Mathematics
1 answer:
seraphim [82]3 years ago
6 0
{-4x+7y+5=-5
{0x-3y=-5 Solve the equation.

{-4x+7y+5=-5
{y=5/3 Substitute the value of y.

-4x+7(5/3)+5=-5 Plug in and solve.

x=65/12 You should get this answer.

Therefore: (x,y) = (65/12,5/3)
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Two sets of three consecutive integers have a property that the product of the larger two is
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Answer:

{1, 2, 3},  {3, 4, 5}

Step-by-step explanation:

Write expressions for three consecutive integers:  n, n + 1, n + 2.

Set up an equation for the verbal description: the product (mulitplication) of the two larger integers (the last two) is one less than 7 times the smallest (the first one).

(n + 1)(n + 2) = 7n - 1

Multiply (FOIL) the left side.

n^2 + 3n + 2 = 7n - 1

Subtract 7n and subtract 1 to make the right side 0.

n^2 - 4n + 3 = 0

Factor.

(n - 1)(n - 3) = 0

Set the two factors equal to 0

n - 1 = 0,  n - 3 = 0

Solve for n.

n = 1,  n = 3

One set of integers begins with 1, so it's {1, 2, 3}.

The other set begins with 3, so it's {3, 4, 5}

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3 years ago
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