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Solve the system of equation by the addition method x-2y=11 and -x+6y =-31

Sonbull [250]

Answer: x = 1, y = - 5

Step-by-step explanation:

The given system of linear equations is expressed as

x - 2y = 11- - - - - - - - - - - - -1

- x + 6y = - 31- - - - - - - - - - - -2

We would eliminate x by adding equation 1 to equation 2. It becomes

- 2y + 6y = 11 - 31

4y = - 20

Dividing the the left hand side and the right hand side of the equation by 4, it becomes

4y/4 = - 20/4

y = - 5

Substituting y = - 5 into equation 1, it becomes

x - 2 × - 5 = 11

x + 10 = 11

Subtracting 10 from the left hand side and the right hand side of the equation, it becomes

x + 10 - 10 = 11 - 10

x = 1

3 0

4 years ago

The cost of a family membership at a health club is 58$ per month plus a one-time 129$ start-up fee. If a family spent 651$, how

kramer

9 months.
$651 - $129 = $522
$522/$58 = 9

3 0

3 years ago

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A student uses four different tape-measures to estimate the length of a ruler manufactured to be exactly 1 foot long. Which meas

Scrat [10]

B) 12 inches would be the most accurate measurement.

Since the ruler is exactly 1 foot long, the most accurate measurement is 12 inches. 12.005 is a tempting answer, since it is the most specific/exact, but 12 inches is the most accurate, since this is equal to exactly one foot.

7 0

3 years ago

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A restaurant owner was experimenting with the taste of her homestyle lemon drink. She started with 60 litres of water. She remov

Burka [1]

Answer:

ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

Step-by-step explanation:

In order to solve the final ratio of lemon juice to water, let us start by determining the initial ratio of pure lemon juice to water in the first mix. This is done as follows:

Total volume of mixture = 60 liters

initial volume of water = 60 liters

initial volume of lemon juice = 0 liters

1) She removed 15 liters of the water and replaced it with 15 liters of pure lemon juice.

Volume of water = 60 - 15 = 45 liters

Volume of lemon juice = 15 liters

$\therefore \frac{15}{60}\ = \frac{1}{4}\ of\ the\ first\ mix\ is\ lemon\ juice\\\frac{45}{60}\ = \frac{3}{4}\ of\ the\ first\ mix\ is\ pure\ water$

2) She removed 10 liters of the new mixture

Let us convert this amount removed into ratio:

$lemon\ juice\ = \frac{1}{4}\ \times 10 = \frac{10}{4} = \frac{5}{2}\ liters.\\ \therefore the\ owner\ removes\ \frac{5}{2}\ liters\ of\ pure\ lemon\ juice\\pure\ water\ = \frac{3}{4}\ \times 10 = \frac{30}{4} = \frac{15}{2}\ liters\\ \therefore\ the\ owner\ removes\ \frac{15}{2}\ liters\ of\ water\ from\ the\ first\ mix.$

New volumes of water and lemon juice after removing the 10 liters of mixture is calculated as follows:

$lemon\ juice\ = 15 - \frac{5}{2} = \frac{30-5}{2} = \frac{25}{2}\ liters\ of\ lemon\ juice\\pure\ water\ = 45 - \frac{15}{2} = \frac{90-15}{2} = \frac{75}{2}\ liters\ of\ pure\ water$

3) and replaced it with 10 liters of water.

$New\ volume\ of\ water\ = 10 + \frac{75}{2} = \frac{20+ 75}{2} = \frac{95}{2}\ liters$

The final ratio of lemon juice to water:

$\frac{25}{2} : \frac{95}{2}\\= 25 : 95\\= 5 : 19$

Therefore, the final ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

4 0

3 years ago

Solve this with elimination please, 3x + 6y = 6

Dafna1 [17]

Times 2nd equation by 2
add to first equation

3x+6y=6
<u>4x-6y=8 +</u>
7x+0y=14

7x=14
divide both sides by 7
x=2

sub back

2x-3y=4
2(2)-3y=4
4-3y=4
minus 4 both sideds
-3y=0
y=0

(x,y)
(2,0)

8 0

3 years ago

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