All categories

3 years ago

Use elimination to solve each system of equations.

Mathematics

2 answers:

AVprozaik [17]3 years ago

8 0

2x - y = -1

3x - 2y = 1

Multiply the first equation by -2

-4x + 2y = 2

Add the new equation to the second equation

-x = 3

x = -3

Plug -3 into the first equation

2 * -3 - y = -1

-6 - y = -1

-y = 5

y = -5

Doss [256]3 years ago

3 0

Answer:

(-3, -5)

Step-by-step explanation:

Elimination essentially means that we need to eliminate one variable so that we're left with only one to deal with. For this problem, let's eliminate y.

Multiply the first equation by 2:

2 * (2x - y) = (-1) * 2

4x - 2y = -2

Now, subtract the second equation from this new "first" equation:

4x - 2y = -2

- 3x - 2y = 1

_____________

x + 0y = -3

So, we see that x = -3. We can now substitute this value of x into one of the equations and solve for y:

2x - y = -1

2 * (-3) - y = -1

-6 - y = -1

y = -5

Thus, the solution is (-3, -5).

Hope this helps!

You might be interested in

What would be the total cost, both fixed and variable, at an activity level of 7,100 units? Assume that this level of activity i

monitta

Answer:

TC = $971,919

Step-by-step explanation:

Given complete question is as follows:

" Cooke Corporation reports that at an activity level of 7,000 units, the total variable cost is $590,730, and the total fixed cost is $372,750.

What would be the total cost, both fixed and variable, at an activity level of 7,100 units? Assume that this level of activity is within the relevant range."

Solution:

- The total cost (TC) is the sum of the fixed cost (FC) and variable cost (VC):

TC = FC + VC

- The fixed cost remains constant at every unit level i.e [email protected],000 = [email protected],100 = $372,750.

- The variable cost VC is a linear function of number of units. The marginal variable cost (MVC) is:

MVC = VC / numbe of units

MVC = 590,730 / 7000

MVC = $84.39/units

- The VC cost @7,100 units is as follows:

[email protected],100 = [email protected],000 + MVC*( 7,100 - 7,000)

[email protected],100 = $590,730 + $84.39/units*( 100 )

[email protected],100 = $590,730 + $8439

[email protected],100 = $599,169

- The total cost for 7,100 units is:

TC = FC + VC

TC = $372,750 + $599,169

TC = $971,919

6 0

4 years ago

2 The point C ( − 3 , − 1 ) C(−3, −1) is rotated 18 0 ∘ 180 ∘ clockwise about the origin. What are the coordinates of the res

Mekhanik [1.2K]

Answer:

Step-by-step explanation:

If we have the coordinate (x,y), if this coordinate is rotated by 180 degrees clockwise, the resulting coordinate will be expressed as (-x, -y) i.e the original coordinate axis are both negated.

Given the coordinate C(-3, -1), if this coordinate is rotated clockwise about the origin, the coordinate of the resulting point will be at C' (-(-3), -(-1))

C' (-(-3), -(-1))

C' = (3, 1)

Hence option A is correct

8 0

3 years ago

Suppose a researcher is testing a new vaccine on mice to see how well it prevents the flu virus. The lab has 1000 mice available

AfilCa [17]

Solution :

Sampling may be defined as the technique of selecting the individual members or the subset of the population to make a statistical inferences and estimates the characteristics of the entire population.

There are several sampling methods. This includes : Systematic sampling, clustered sampling, stratified sampling, quota sampling, judgement sampling, random sampling, convenience sampling and many more.

In the context, the sampling methods for each of the descriptions are :

a). The researcher use computer program to randomly choose a sample of 30 mice of the 1000 mice for using her study

--- Simple Random

b). The researcher chose the 1st 30 mice as she can reach the door to the mouse room

--- Convenience sampling

c). The mice those whose are kept in the cages on 10 various shelves in mouse room. The researcher or the experimenter chose the three mice from each shelve.

---- Stratified sampling

d). Each of the cage have 5 mice and the researcher randomly chooses 6 cages for her study

----- Cluster sampling

e). The researcher generates the list of the identification numbers which has been sorted from the smallest to the largest. The researcher randomly picks 1 mouse form the list and selects every 4 mouse until the researcher has 30 mice.

---- Systematic sampling

7 0

3 years ago

Look at the equation below. How many solutions are there?<br><br> 2(3x+4)=6x+8)

SOVA2 [1]

Answer:

x∈R

Step-by-step explanation:

2(3x+4)=6x+8

Use the distributive property to multiply 2 by 3x+4.

6x+8=6x+8

Subtract 6x from both sides.

6x+8−6x=8

Combine 6x and −6x to get 0.

8=8

Compare 8 and 8.

True

This is true for any x.

x∈R

6 0

3 years ago

Read 2 more answers

What are the answers plz help im failing this class badly plz help plzzzz comeon

igomit [66]

Ok so f(x) and g(x) are the same thing as y. this means that you can solve these equations the same as any other multi-step equation. the only difference is if they have a number other than x in the parentheses. if they have a number you will just replace the x’s in the equation with the number in the parentheses.

example:

regular equation equation with f(4)
f(x)=2x+1 f(4)=2(4)+1

make sure to use pemdas :)

4 0

3 years ago