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3 years ago

Enter the variable that is easiest to solve for in this system of equations. 6y=10x+5 , 6y=5x+7

Mathematics

2 answers:

djverab [1.8K]3 years ago

8 0

Answer:

Step-by-step explanation:

nhmnj

Rudik [331]3 years ago

5 0

Answer:

(2/5, 9/6)

Step-by-step explanation:

6y = 10x + 5 | 6y = 5x + 7

Set them equal to each other because 6y = 6y.

10x +5 = 5x + 7

5x = 2

x = 2/5

6y = 5*2/5 + 7

6y = 2 + 7

y = 9/6

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Work Shown:

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Molodets [167]

Given:

In a set of 3 numbers the first is a positive integer, the second is 3 more than the first and the 3rd is a square of the second.

To find:

The equation for the given situation if the sum of the numbers is 77.

Solution:

a. Let the first number in the set is x.

The second is 3 more than the first. So, the second number is $(x+3)$ .

The 3rd number is a square of the second. So, the third number is $(x+3)^2$ .

Therefore, the first, second and third numbers are $x,(x+3),(x+3)^2$ respectively.

b. The sum of the numbers is 77.

First number + Second number + Third number = 77

c. So, the equation in terms of x is:

$x+(x+3)+(x+3)^2=77$

Therefore, the required equation is $x+(x+3)+(x+3)^2=77$ .

d. On simplification, we get

$x+x+3+x^2+6x+9=77$ $[\because (a+b)^2=a^2+2ab+b^2]$

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Subtract 77 from both sides.

$x^2+8x+12-77=77-77$

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Therefore, the simplified form of the required equation is $x^2+8x-65=0$ .

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