All categories

4 years ago

Use the substitution method to solve the following system of equations:

Mathematics

1 answer:

horsena [70]4 years ago

5 0

Answer:

(6, - 3 )

Step-by-step explanation:

Given the 2 equations

3x + 5y = 3 → (1)

x + 2y = 0 → (2)

Rearrange (2) expressing x in terms of y by subtracting 2y from both sides

x = - 2y → (3)

Substitute x = - 2y into (1)

3(- 2y) + 5y = 3

- 6y + 5y = 3

- y = 3 ( multiply both sides by - 1 )

y = - 3

Substitute y = - 3 into (3) for corresponding value of x

x = - 2(- 3) = 6

Solution is (6, - 3 )

You might be interested in

the tens digit of a two digit number is 5 greater the units digit. If you subtract double the reversed number from it, the resul

likoan [24]

Given:

The tens digit of a two digit number is 5 greater the units digit.

If you subtract double the reversed number from it, the result is a fourth of the original number.

To find:

The original number.

Solution:

Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:

$n=(x+5)\times 10+x\times 1$

$n=10x+50+x$

$n=11x+50$

Reversed number is:

$x\times 10+(x+5)\times 1=10x+x+5$

$x\times 10+(x+5)\times 1=11x+5$

If you subtract double the reversed number from it, the result is a fourth of the original number.

$11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)$

$11x+50-22x-10=\dfrac{1}{4}(11x+50)$

$40-11x=\dfrac{1}{4}(11x+50)$

Multiply both sides by 4.

$160-44x=11x+50$

$160-50=11x+44x$

$110=55x$

Divide both sides by 55.

$\dfrac{110}{55}=x$

$2=x$

The unit digit is 2. So, the tens digit is $2+5=7$ .

Therefore, the original number is 72.

6 0

3 years ago

Solve the inequality 15 ≥ q + 3

oksano4ka [1.4K]

Answer:

$q\le \:12$

Step-by-step explanation:

<u>Solving</u>

$\mathrm{Switch\:sides}$ (Not a required step)

$q+3\le \:15$

$\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}$

$q+3-3\le \:15-3\\=q\le \:12$

$\bold{q\le \:12}$

<u>Graphing</u>

5 0

2 years ago

The new patio at Tonya's house is 5 yards long by 10 feet wide. She is going to cover the patio with square bricks that measure

Klio2033 [76]

Answer:

Step-by-step explanation:

Steps to take to determine the answer

Because the length is in yards, it has to be converted to foot
Find the area of the patio using the length and width measured in foot
Determine the area of the square brick
Multiply the cost of the brick by the area

1 yards = 3 foot

5 x 3 = 15 foot

Area of a rectangle = length x breadth

15 x 10 = 150 ft^2

Cost = 150 x 4 = $600

4 0

3 years ago

Bob's desk had 11/12 grams of dust on it. He wiped away 1/12 grams of the dust. How many grams of dust are left on his desk? Wri

mars1129 [50]

Answer:

5/6 are left

Step-by-step explanation:

5 0

3 years ago

Rewrite 6(40-10) using distributive property of multiplication over subtract

Stells [14]

Answer:

240-60

Step-by-step explanation:

Multiply both numbers inside the parenthesis by what's on the outside

4 0

3 years ago