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
otez555 [7]
2 years ago
10

5x + 3y = 16 3x -5y = -4 How do I solve this

Mathematics
1 answer:
lawyer [7]2 years ago
6 0

Answer:

(2, 2)

Step-by-step explanation:

We can solve this system of equations using the elimination method.

Let's start by multiplying the first equation by 3:

3(5x+3y)=3(16)\\3(5x)+3(3y)=48\\15x+9y=48

Now, multiply the second equation by 5:

5(3x-5y)=5(-4)\\5(3x)-5(5y)=-20\\15x-25y=-20

Since both equations have 15x, we can eliminate the x by subtracting the two equations.

15x-15x+9y-(-25y)=48-(-20)\\9y+25y=68\\34y=68\\\text{Divide both sides by 34}\\y=2

Now, substitute 2 for y to solve for x:

5x+3y=16\\5x+3(2)=16\\5x+6=16\\\text{Subtract 6 from both sides}\\5x=10\\\text{Divide both sides by 2}\\x=2

Therefore the solution to this system of equations is:

(x, y)=(2, 2)

You might be interested in
Let A, B, C and D be sets. Prove that A \ B and C \ D are disjoint if and only if A ∩ C ⊆ B ∪ D
ANEK [815]

Step-by-step explanation:

We have to prove both implications of the affirmation.

1) Let's assume that A \ B and C \ D are disjoint, we have to prove that A ∩ C ⊆ B ∪ D.

We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

Therefore, x ∈ (A \ B) ∩ (C \ D), absurd!

It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

The absurd came from assuming that A ∩ C ⊄ B ∪ D.

That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that  A \ B ∩ C \ D is not empty. That means there is an element x that belongs to  A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

As x ∈ A \ B, x belongs to A but x doesn't belong to B.  

As x ∈ C \ D, x belongs to C but x doesn't belong to D.

With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

It's absurd because we were assuming that A ∩ C ⊆ B ∪ D, therefore every element of A ∩ C must belong to B ∪ D.

The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

7 0
3 years ago
Simplify: <img src="https://tex.z-dn.net/?f=4%5Csqrt%7B12%7D%20-%20%5Csqrt%7B3%7D%20%2B%204%20%5Csqrt%7B6%7D%20%2B%203%20%5Csqrt
Dahasolnce [82]
4 divided by 12 -3+4 divided by 6+3 divided by 4
6 0
2 years ago
Plz help! Answer at least one of these questions and i will give you brainly! It’s ok if you don’t know them all!
FinnZ [79.3K]
For number 3 it is 56 pints! i’ll do the other ones in a second
8 0
3 years ago
Read 2 more answers
Find the of x in each triangle.
zhannawk [14.2K]
I pretty sure you either add or subtract to get the answer
7 0
3 years ago
Read 2 more answers
Which graph correctly represents 1/3y-1/2x&gt;2
Sladkaya [172]
A graph with a dotted line running through the points (-4, 0) and (0, 6) shaded above the origin.

6 0
3 years ago
Read 2 more answers
Other questions:
  • Stephen's glass holds 450 milliliters of milk. Farrah's glass holds 2\5 as much milk. How much milk does Farrah's glass holds?
    14·1 answer
  • The first pentagon is dilated to form the second pentagon. Drag and drop the answer to correctly complete the statement. IT IS 2
    13·2 answers
  • You move down 2 units and up 7 units. You end at (-1,4). Where did you start?
    14·2 answers
  • 3x exponent 2=48 solve the equation please
    6·2 answers
  • How do you rewrite the equation in the form 52m = 460
    5·1 answer
  • COLLE
    8·1 answer
  • Use the expression below.
    6·1 answer
  • 3v+2u÷5+u-5v÷8-3v÷4​
    5·1 answer
  • A diameter of a circle has endpoints at (-3, 2) and (-3,-3). What are the coordinates of the center
    15·1 answer
  • Which scalelfactors are contractions?<br> -1<br> 3/4<br> -0.5<br> 7
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!