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3 years ago

Solve the following systems using the substitution method.

Mathematics

2 answers:

Inga [223]3 years ago

6 0

Answer:

Step-by-step explanation:

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Nadya [2.5K]3 years ago

6 0

Step-by-step explanation:

2x + 8y = 12 ......... Equation 1

x - 2y = 0 .............. Equation 2

Make x the subject in equation 2 and substitute it into equation 1

That's

x = 2y

We have

2(2y) + 8y = 12

4y + 8y = 12

12y = 12

Divide both sides by 12

y = 1

Substitute y = 1 into x = 2y

That's

x = 2(1)

x = 2

The answers are

x + y = 7......... Equation 1

2x + y = 5 ......... Equation 2

Make y the subject in equation 1 and substitute it into equation 2

We have

y = x - 7

2x + x - 7 = 5

3x = 7 + 5

3x = 12

Divide both sides by 3

x = 4

Substitute x = 4 into y = x - 7

y = 4 - 7

y = - 3

We have the answers as

y = -1/2 + 1 ......... Equation 1

2x + 3y = 6 ........ Equation 2

From equation 1

y = 1/2

Substitute y = 1/2 into Equation 2

So we have

2x + 3(1/2) = 6

2x + 3/2 = 6

2x = 6 - 3/2

2x = 9/2

Divide both sides by 2

x = 9/4

The answers are

2x - 1/3y = - 9.......... Equation 1

-3x + y = 15 ........... Equation 2

Make y the subject in equation 2 and substitute it into equation 1

That's

y = 15 + 3x

2x - 1/3( 15 + 3x) = - 9

2x - 5 - x = - 9

x = - 9 + 5

x = - 4

Substitute x = - 4 into y = 15 + 3x

That's

y = 15 + 3(-4)

y = 15 - 12

y = 3

The answers are

Hope this helps you

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What is the value of the following expression 7+18÷(6-3)

mixer [17]

First you do 6-3 which is 3 then divide it by 18 which is 6 then add it by 7 which is 13

5 0

3 years ago

Read 2 more answers

Please help me solve this

Viktor [21]

You can factor the 32 out of the sum:

$\displaystyle \sum_{m=1}^\infty 32 \cdot \left(\dfrac{1}{2}\right)^{m-1} = 32\sum_{m=1}^\infty \left(\dfrac{1}{2}\right)^{m-1}$

We can also change the index as follows

$\displaystyle 32\sum_{m=1}^\infty \left(\dfrac{1}{2}\right)^{m-1} = 32\sum_{m=0}^\infty \left(\dfrac{1}{2}\right)^{m}$

Now, we have a theorem that states that the series

$\displaystyle \sum_{m=1}^\infty a^m$

converges if and only if $|a|$ , and in this case we have

$\displaystyle \sum_{m=1}^\infty a^m = \dfrac{1}{1-a}$

This is your case, because you have

$|a|=\dfrac{1}{2}$

which implies that your series converges, and the value is

$\displaystyle 32\sum_{m=0}^\infty \left(\dfrac{1}{2}\right)^{m} = 32 \cdot \dfrac{1}{1-\frac{1}{2}} = 32\cdot 2 = 64$

3 0

3 years ago

What is the slope of the line passing thru the points (-6,-5) (4,4)

Katena32 [7]

Answer:

slope = $\frac{9}{10}$

Step-by-step explanation:

Calculate the slope m using the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 5) and (x₂, y₂ ) = (4, 4)

m= $\frac{4+5}{4+6}$ = $\frac{9}{10}$

8 0

3 years ago

The nut shack sells cashews for $6.00 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to mak

Kay [80]

Answer:

Number of pounds of cashews = x = 14.96 pounds

Number of pounds of Brazil nuts = y = 19.04 pounds

Step-by-step explanation:

Let us represent:

Number of pounds of cashews = x

Number of pounds of Brazil nuts = y

The nut shack sells cashews for $6.00 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 34 pound mixture that sells for $5.44 per pound

Our system of equations is given as:

x + y = 34...... Equation 1

x = 34 - y

6x + 5y = 34 × 5.44

6x + 5y = 184.96.......Equation 2

Ww substitute : 34 - y for x in Equation 2

6(34 - y) + 5y = 184.96

204 - 6y + 5y = 184.96

Collect like terms

- 6y + 5y = 184.96 - 204

-y = -19.04

y = 19.04 pounds

Solving for x

x = 34 - y

x = 34 - 19.04

x = 14.96 pounds

Number of pounds of cashews = x = 14.96 pounds

Number of pounds of Brazil nuts = y = 19.04 pounds

7 0

3 years ago

Q15. Ken earned x dollars at his part-time job on Friday. His wife earned $12 more

mafiozo [28]

Ken earns 54 dollars at his part-time job on Friday

Given that Total amount earned by ken and his wife at their part-time job on Friday= $174

Money earned by ken= x dollars

Money earned by ken's wife = (2x+12) dollars

Total amount earned by ken and his wife at their part-time job on Friday= x dollars + (2x+12) dollars

(x + 2x + 12 ) dollars = $ 174 ( addition of ken and ken's wife income and total amount earned by ken and his wife at their part-time job on Friday is $174)

(3x + 12 ) dollars = $ 174

3x=$162

x= $\frac{162}{3}$

x= 54 dollars

Therefore,54 dollars were earned by ken at his part-time job on Friday

Hence,Ken earns 54 dollars at his part-time job on Friday

Learn more about dollars here:

brainly.com/question/14982791

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4 0

1 year ago