# A student took a system of equations, multiplied the first equation 2 by 3 and the second equation by , then added the results together. Based on this, she concluded that there were no solutions. Which system of equations could she have started with? A. -2x+4y=4 -3x+6y=6 B. 3x+y=12 -3x+6y=6 C.3x+6y=9 -2x-4y=4 D.2x-4y=6 -3x+6y=9

C)3x+6y=9

-2x-4y=4

Step-by-step explanation:

A student took a system of equations, multiplied the first equation 2 by 3 and the second equation by , then added the results together.

Lets check with each option

We multiply the first equation by 2  and second equation by 3 and add it.

When both x  and y terms gets cancelled then we can say there were no solutions.

A) -2x+4y=4

-3x+6y=6

Equation becomes

-4x + 8y = 8

-9x + 18y = 18

------------------------

-13x + 26y = 26

B) 3x+y=12

-3x+6y=6

Multiply first equation by 2  and second equation by 3

6x + 2y = 24

-9x + 18x = 18

------------------------

-3x + 20y = 42

C)3x+6y=9

-2x-4y=4

Multiply first equation by 2  and second equation by 3

6x + 12y = 18

-6x - 12y = 12

---------------------------

0 = 30

Both x  and y terms becomes 0. Hence there is no solution for these system of equations.

.3x+6y=9

-2x-4y=4

Step-by-step explanation:

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## Related Questions

Mr Daniels is organizing a class field trip on a budget of \$900.The bus rental costs \$600. Mr.daniels will also buy tickets that will cost \$9.50 per student. Write an inequality to represent the number students,y, that he can bring on the trip.

y ≤ 31 students

Step-by-step explanation:

The rental cost is a fixed cost that will be incurred irrespective of the number of students embarking on the class field trip. This cost added to the total ticket cost must be less than or equal to the budget.

the total ticket cost for y number of students

= 9.5y

Hence the total cost = 9.5y + 600 ( measured in \$)

In inequality form,

9.5y + 600 ≤ 900 (all in \$)

9.5y ≤ 900 - 600

9.5y ≤ 300

y ≤ 300/9.5

y ≤ 31 students

600 + 9.5x (less than or equal to) 900

600 fixed amount
9.5 is the variable changing amount and differs among number of students taken

alis dog weighs 8 times as much as her cat. together, the two pets weigh 54 pynds. how much does Alis dog weigh?

The weight of the Alis dog is pounds.

Further explanation:

Consider the weight of the Alis dog as pounds and weight of the cat as pounds.

Since, the weight of the Alis dog is 8 times the weight of the cat. It can be written as follows:

......(1)

Now, the total weight of the cat and dog are given as 54 pounds. It can be written as follows:

......(2)

From equation (1), substitute for in equation (2).

Thus, the weight of the cat is 6 pounds.

Substitute 6 for in equation (1) to obtain the weight of Alis dog as follows:

Thus, the weight of the Alis dog is 48 pounds.

1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

brainly.com/question/1632445

2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12

brainly.com/question/1473992

3. What are the domain and range of the function f(x) = 3x + 5?

brainly.com/question/3412497

Subject: Mathematics .

Chapter: linear equation.

Keywords:

lines, equation, pound, Alis dog, cat, weight, linear equation, zeros, x,y,x=8y,x+y=54, function, substitution, pets, direct substitution, elimination, graph, middle term factorization, fraction.

Find the equation of a plane that is perpendicular to the vector −4i⃗ −4j⃗ −k⃗ and passing through the point (−2,−5,5)

-4x - 4y - z = 23 is the equation of the plane that is perpendicular to the vector −4i− 4j − k and passing through the point (−2, −5, 5)

What is Vectors?

Vector is a quantity in mathematics which has both direction and magnitude contrary to the scalar which has only magnitude.

Equation of a plane passing through a point (x₁, y₁, z₁) and perpendicular to the vector a i^ + b j^ + c k^ is.

a (x - x₁) + b (y - y₁) + c (z - z₁) = 0

Here we have the point (-2, -5, 5)

Normal vector = −4i− 4j − k

Equation of the plane perpendicular to the vector −4i− 4j − k and passing through (-2, -5, 5) is,

⇒ -4 (x - -2) + -4 (y - -5) + -1 (z - 5) = 0

⇒ -4 (x + 2) - 4 (y + 5) - 1 (z - 5) = 0

⇒ -4x - 8 - 4y - 20 - z + 5 = 0

⇒ -4x - 4y - z - 23 = 0

⇒ -4x - 4y - z = 23

Hence the equation of the plane that is perpendicular to the vector −4i− 4j − k and passing through the point (−2, −5, 5) is -4x - 4y - z = 23.

brainly.com/question/13322477

#SPJ5

hello ....

the equation of a plane that is ;  ax+by+cz +d =0

the vector perpendicular to this plane is : V(a,b,c)

in this exercice ; a = -4  b= -4  c = -1

then: the equation of a plane that is ;  -4x-4y-z +d =0

but the plane  passing through the point (−2,−5,5) :

-4(-2)-4(-5)-(5) +d =0

23+d =0

d =-23

the equation of a plane is : -4x-4y-z-23 =0

A washer and dryer cost \$891 combined. The washer costs \$41 more than the dryer. What is the cost of the dryer?

The dryer cost is:\$425
The dryer costs \$425 because 891-41=850, and 850/2=425. Hope this helped!

How many solutions does the equation have?y+7=y–3many solutions1 solutionno solutions?

No solution
Subtract y on both sides, giving you...
7= -3
Which is false

A team has P points. P = 3W + D

W = Wins
D = Draws

B) After 35 games a different football team has 50 points. 14 games were draw. How many games has this team lost

There were 12 wins. If they played 35 games, 12 were won and 14 were drawn, you just subtract them from 35 and you get 9. The team lost 9 games.

BUSit

Step-by-step explanation:

A bag contains six real diamonds and five fake diamonds. If six diamonds are picked from the bag at random, what is the probability that at most four of them are real?

Step-by-step explanation:  Given that a bag contains 11 diamonds, out of which 6 are real and 5 are fake. 6 diamonds are picked from the bag randomly. We are to calculate the probability that at most four of the 6 diamonds are real.

Since we can choose at most 4 real diamonds, so the number of ways in which we can do so is given by

And the total number of ways in which we can choose 6 diamonds out of 11 is

Therefore, the required probability will be

Thus, the probability is 77% approx.

2−3−40 ÷ 2+13+40 2+8−20 2+12+20