Consider the following system of equations. x+y=11 and 2x - 3y=-3. which equation can be added to the system so that the solution does not change.

a) x-y=2
b) -2x+2y=-2
c)3x+y=20
d)x+2y=18

B) -2x+2y=-2

Step-by-step explanation:

we have

----> equation A

----> equation B

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (6,5)

see the attached figure

Remember that

If a equation is added to the system so that the solution does not change, then the solution of the system must be a solution of the equation added

Verify each case

The solution of the system is (6,5)

substitute the value of x and the value of y in each equation

case A) x-y=2

6-5=2

1=2 ----> is not true

therefore

This equation can't be added to the system

case B) -2x+2y=-2

-2(6)+2(5)=-2

-12+10=-2

-2=-2 ----> is true

therefore

This equation can be added to the system

case C) 3x+y=20

3(6)+5=20

18+5=20

23=20 ----> is not true

therefore

This equation can't be added to the system

case D) x+2y=18

5+2(6)=18

5+12=18

17=18 ----> is not true

therefore

This equation can't be added to the system

answer: i think you should do the math and pay attention in class : )

step-by-step explanation:

that is truly what   think but if i get the answer i will

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.