MATHEMATICS MIDDLE SCHOOL

What is the solution to the system of equations?-3x + y = -1
2x + y = 14

a (3, 8)
b (-8, 3)
c (-3, 8)
d (8, 3)

Answers

Answer 1

Answer: a (3,8)
solution below

Answer 2

Answer:

Answer:

The answer is A.

Step-by-step explanation:

I used the elimination method to solve this system of equations.

The elimination method is where you add both of the equations, where one of the variables are equal in terms of number, but the signs are flipped. That's because you add the equations, crossing out one of the variables, leaving you with one variable to easily solve with.

It goes like this:

I multiplied the first equation (-3x+y=-1) by -1, to be able to cross out the y variable when I add.

So, after multiplying, the equation would be: 3x-y=1

Now, you add the two equations together.

3x-y=1

2x+y=14

+________

5x=15

Solving we get x=3.

That already gives you a as an answer, but let's continue.

Now we plug x=3 back into one of the equations to find what y is.

2(3)+y=14

6+y=14

y=8

So, the answer is A, (3, 8).

Checking: Just plug the numbers back in to see if they're right.

-3(3)+8= -1

-9+8=-1

-1=-1

Hope this helps!

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how can you write the equation for a linear function if you know only two ordered pairs for the function

Answers

Answer:

yes, you can :)

Step-by-step explanation:

A vendor sells 60 pieces of fruit that are either apples or oranges. The ratio of apples to oranges is 3: 2. How many apples did the vendor sell? How many oranges did the vendor sell?

Answers

so 60 fruitsthe ratio is apples to oranges=3:2they are simplified so they have 3 apple units to 2 orange unitstherefor60=2+3=5 fruit unitsdividd 60 by 5 to find 1 fruit unit60/5=12apples=3 unitsapples=3 times 12=36oranges=2 unitsoranges=2 times 12=2436 apples and 24 oranges

ok so 3:2 is just the ratio and is a simplified answer and I am going to divide 60÷2 and 60÷3 to get my answer. So 60÷2=30 and 60÷3=20 so another way of saying 3:2 is 20:30 and since it is apples to oranges, there is 20 apples and there is 30 oranges.

each box of party invitations cost $6 Jenny bought three boxes of invitations she paid with a $20 bill complete the number sentences to find out to find how much change Jenny got

Answers

Answer:

jenny gets $2 in change because $6 times 3 is 18 and 20-18 is 2. I hope this helps

Step-by-step explanation:

If P(A) = 0.996, what is the value of P(A)?

Answers

Answer:

$p(a) = 0$

Step-by-step explanation:

$p(a) = 0.966$

Find the derivative of the fraction

$p(a) = (d)/(da) ( 0.966)$

Convert the decimal number to a fraction

$p(a) = (d)/(da) ( (249)/(250) )$

The derivative of a constant is always 0

$p(a) = 0$

A drawer has some red, green, and blue marbles. There are 33 marbles.There are 4 times as many red marbles as green marbles. There are half
as many blue marbles as green marbles. How many blue marbles are in
the drawer?

Answers

Green marbles = x.
There are 4 times as many red marbles as green marbles, so red marbles = 4x.
There are half as many blue marbles as green marbles, so blue marbles = 0.5x
There are 33 marbles in total, so x+4x+0.5x=33.

$x+4x+0.5x=33 \n 5.5x=33 \n x=(33)/(5.5)=(330)/(55)=(30 * 11)/(5 * 11)=(30)/(5)=6 \n \n0.5x=0.5 * 6=3$

There are 3 blue marbles.

so number of red is represented by r
number of green is represented by g
number of blue is represented by b

so r+g+b=33

there are 4 times as many red as green or
r=4g
there are half as many blue as green
1/2g=b or g=2b

so r+g+b=33
we can subsitute 1/2g=b for b
r+g+1/2g=33
subsitute r=4g for r in the equation
4g+g+1/2g=33
add like terms
5 1/2g=33
multiply both sides by 2
11g=66
divide both sides by 11
g=6

there are 6 green marbles

subsitute g=6 into r=4g and g=2b

r=4(6)
r=24
there are 24 red marbles

g=2b
6=2b
divide both sides by 2
3=b
threre are 3 blue marbles

there are 24 red marbles, 6 green marbles, and 3 blue marbles and 24+6+3=33
r=24
g=6
b=3

Simplify the expression. x2/3 · x7/2