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4 years ago

Solve the system by elimination state whether the system has one solution infinite solutions or no solution x+3y=-5 4x-y=6

Mathematics

1 answer:

STatiana [176]4 years ago

8 0

Answer:

one solution, i.e x = 1 and y = -2

Step-by-step explanation:

Given two equations :

x+3y = -5 -------(1)

4x - y =6 ---------(2)

Using elimination method,

Multiply equation (2) by 3 and add it to equation (1)

We get,

x + 3y + {(4x - y)×3} = -5 +(6×3)

x + 12x + 3y - 3y = -5 + 18

13x = 13

x = 13/13 = 1

And corresponding y will be:

x + 3y = -5 , Plug x =1 to get y

1 + 3y = -5

3y = -5 - 1

y = -6/3 = -2

Hence we got only one solution, i.e x =1 and y = -2

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At the grocery store, Alan can buy 4 cans of soup for $2. At the warehouse store the same soup costs $5.76 for 12 cans, which pl

Damm [24]

Answer:

The warehouse has a better price

Step-by-step explanation:

It has a better price because each can at the grocery store is $0.50, the warehouse sells each can for $0.48. The difference is $0.02.

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3 years ago

Which of the following are NOT the lengths of the sides of a triangle?

Evgesh-ka [11]

2,3,6 because 2 and 3 cant equal 6

7 0

3 years ago

Need help with this problem!!

Nezavi [6.7K]

Answer:

Area:

4 x 4 = 16

Finding area of semi circle:

4 is your diameter so half of it is your radius which is 2 since half of 4 is 2!

2^2<---your radius being squared = 4

4(radius squared) x 3.14(pi) = 12.56

12.56 divided by 2 since its a semi circle is = 6.28

6.28 + 16 = 22.28 is your area

Perimeter is:

4 + 4 + 4 (all sides of a square are equal therefore one or two given lengths will be all the sides) = 12

Circumference:

Radius is 2,

2(you just always have to multiply this number when finding circumference) x 3.14(pi) x 2(radius), 2 x 3.14 x 2 = 12.56

12.56 divided by 2 = 6.28

6.28 + 12 = 18.28 is your perimeter.

Just a refresh:

Circumference Formula:

2(always use this number when finding circumference) x pi(3.14 or 22/7 depending on what they tell you to use for pi) x radius

Area of a Circle Formula:

Radius squared x pi(3.14 or 22/7 whatever they tell you to use for pi)

Another thing you should remember:

Whenever it gives you 1/4 of a circle or 1/3 or a semi circle or any fraction, REMEMBER TO DIVIDE BY THAT DENOMINATOR TO WHAT YOU GET FROM EITHER CIRCUMFERENCE OR AREA OF A CIRCLE!

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3 years ago

Can you help me figure out this question I’ve been stuck on this for 20 minutes

Masteriza [31]

Step-by-step explanation:

$\dfrac{2x^2+x-6}{x+x-6} = \dfrac{(2x-3)(x+2)}{2(x-3)}$

3 0

3 years ago

Show that an integer is divisible by 11 if and only if the alternating sum (add first digit, subtract the second, add the third,

Bess [88]

Answer and Step-by-step explanation:

Suppose that we have a number y which is a positive integer and that:

y = $x_n...x_5x_4x_3x_2x_1x_0$

Where;

$x_{0}$ = digit at 10⁰ => one's place (units place)

$x_1$ = digit at 10¹ => 10's place (tens place)

$x_{2}$ = digit at 10² => 100's place (hundreds place)

$x_{3}$ = digit at 10³ => 1000's place (thousands place)

$x_{n}$ = digit at 10ⁿ place

Then;

y = $x_{0}$ * 10⁰ + $x_1$ * 10¹ + $x_{2}$ * 10² + $x_{3}$ * 10³ + $x_{4}$ * 10⁴ + $x_5$ * 10⁵ + . . . + $x_{n}$ * 10ⁿ

Since 10⁰ = 1, let's rewrite y as follows;

y = $x_{0}$ + $x_1$ * 10¹ + $x_{2}$ * 10² + $x_{3}$ * 10³ + $x_{4}$ * 10⁴ + $x_5$ * 10⁵ + . . . + $x_{n}$ * 10ⁿ

Now, to test if y is divisible by 11, replace 10 in the equation above by -1. Since 10 divided by 11 gives -1 (mod 11) [mod means modulus]

y = $x_{0}$ + $x_1$ * (-1)¹ + $x_{2}$ * (-1)² + $x_{3}$ * (-1)³ + $x_{4}$ * (-1)⁴ + $x_5$ * (-1)⁵ + . . . + $x_{n}$ * (-1)ⁿ

=> y = $x_{0}$ - $x_1$ + $x_{2}$ - $x_{3}$ + $x_{4}$ - $x_5$ + . . . + $x_{n}$ (-1)ⁿ (mod 11)

Therefore, it can be seen that, y is divisible by 11 if and only if alternating sum of its digits $x_{0}$ - $x_1$ + $x_{2}$ - $x_{3}$ + $x_{4}$ - $x_5$ + . . . + $x_{n}$ (-1)ⁿ is divisible by 11

Let's take an example

Check if the following is divisible by 11.

i. 1859

Solution

1859 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (1 - 8 + 5 - 9) is divisible by 11.

1 - 8 + 5 - 9 = -11.

Since -11 is divisible by 11 so is 1859

ii. 31415

Solution

31415 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (3 - 1 + 4 - 1 + 5) is divisible by 11.

3 - 1 + 4 - 1 + 5 = 10.

Since 10 is not divisible by 11 so is 31415 not divisible.

3 0

4 years ago