1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sweet [91]
3 years ago
15

Solve by elimination -3x+2y=10 -2x-y=-5

Mathematics
1 answer:
Nataly [62]3 years ago
6 0
First you need to get two similar terms to eliminate, I'll do y:
-3x + 2y = 10
-4x - 2y= -10
And then you minus
x = 20
Now you can substitute x in to one of the equations to find y:
-60 + 2y = 10
+ 60
2y = 70
÷ 2
y = 35
So your values are y = 35 and x = 20. Hope this helps!
You might be interested in
Sally paid the following bills rent $450.00 cell phone $37.50 and cable $69.99 how much money did she pay ?
romanna [79]

Answer:

557.49

Step-by-step explanation:

Add the three bills together

450.00

 37.50

 69.99

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

557.49

3 0
3 years ago
The table shows the number of pounds of green
mel-nik [20]

Answer:

10 1/2

Step-by-step explanation:

First you would do.

9+2/3+5/6

2/3=4/6

9+4/6+5/6

9+9/6=3/2

9+1 1/2

=10 1/2

3 0
3 years ago
Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .
kogti [31]

Answer:

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

a is an arbitrary prime number. (1)

b = \sqrt{1 + 2\cdot a \cdot c} (2)

c is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if (x+y)^{2} = x^{2} + 2\cdot x\cdot y  + y^{2}. From statement, we must fulfill the following identity:

a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}

By Associative and Commutative properties, we can reorganize the expression as follows:

a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2} (1)

Then, we have the following system of equations:

x = a (2)

(b^{2}-1) = 2\cdot x\cdot y (3)

y = c (4)

By (2) and (4) in (3), we have the following expression:

(b^{2} - 1) = 2\cdot a \cdot c

b^{2} = 1 + 2\cdot a \cdot c

b = \sqrt{1 + 2\cdot a\cdot c}

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, a, b, c > 1. If a, b and c are prime numbers, then  2\cdot a\cdot c must be an even composite number, which means that a and c can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, b must be a natural number, which means that:

1 + 2\cdot a\cdot c \ge 4

2\cdot a \cdot c \ge 3

a\cdot c \ge \frac{3}{2}

But the lowest possible product made by two prime numbers is 2^{2} = 4. Hence, a\cdot c \ge 4.

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

a is an arbitrary prime number. (1)

b = \sqrt{1 + 2\cdot a \cdot c} (2)

c is another arbitrary prime number. (3)

Example: a = 2, c = 2

b = \sqrt{1 + 2\cdot (2)\cdot (2)}

b = 3

4 0
3 years ago
A coordinate map of the local grocery store is shown below. Ice cream is located at the point (-8,0)(−8,0)left parenthesis, minu
Alona [7]

Answer:

Step-by-step explanation:

If on the coordinate map, ice cream is located at the point (-8,0) and sprinkles are located at the point (-8,6), we can find the distance between the coordinate points using the formula;

D = √(x2-x1)²+(y2-y1)²

Given

x1 = -8, y1 = 0, x2 = -8 and y2 = 6

Substitute

D = √(x2-x1)²+(y2-y1)²

D = √(-8-(-8))²+(6-0)²

D = √0²+6²

D = √36

D = 6units

Hence the distance between the coordinate points is 6units

7 0
3 years ago
Let n be the number of couples dancing in a competition. If there are 5 organizers, which expression represents the total number
Korvikt [17]
2n+5...a couple is two people so you need to multiply the number of couples, n, by 2 to get the total number of dancers. Then add the total number of organizers.
3 0
3 years ago
Other questions:
  • Robert went to visit his friend who lives 170 kilometers away. it took him 2.5 hours to drive to his friends house. at what spee
    14·1 answer
  • Which of the following scenarios represents an impulse purchase?
    14·1 answer
  • In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat
    10·2 answers
  • Which polynomials are in standard form
    8·1 answer
  • How do you change a mixed number to an improper fraction?
    14·1 answer
  • Rosa has $175 in her online music account. Each month she buys $15 worth of new songs. Which inequality could be solved
    14·1 answer
  • I NEED HELPPPPPPPPP AHHHHHHHHHHHHHHHHHHHH<br> please TwT
    11·1 answer
  • Find the area of the unshaded portion of
    13·1 answer
  • My bad i forgot to put the pic
    12·1 answer
  • FIRST ANSWER WILL GET BRAINLIEST In parallelogram EFGH, m∠1 = 3x – 5, m∠2 = x + 10, and m∠3 = 2x + 15.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!