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
DaniilM [7]
2 years ago
12

Solving systems by substitution

Mathematics
1 answer:
Kipish [7]2 years ago
8 0

9514 1404 393

Answer:

  (x, y) = (0, -2)

Step-by-step explanation:

When solving by substitution, you usually want to find an expression for one of the variables in terms of the other. So, the first thing you look for is an equation that has a coefficient of 1 or -1 on one of the variables. Recognizing that the second equation's terms all have a common factor of 3, you basically have two choices.

<h3>Substitute for y</h3>

Using equation 1, you can write an expression for y:

  y = 5x -2 . . . . . . add 5x to both sides

Then substituting this into the original equation 2, you have ...

  -3x +6(5x -2) = -12

  27x -12 = -12 . . . . . . . simplify

  27x = 0 . . . . . . . . . add 12

  x = 0 . . . . . . . . .  divide by 27

  y = 5(0) -2 = -2 . . . . find y using the expression for substitution

The solution is (x, y) = (0, -2).

__

<h3>Substitute for x</h3>

If you decide you'd rather substitute for x, you can solve the second equation easily for x.

  -3x +6y = -12

  x -2y = 4 . . . . . . divide by -3

  x = 2y +4 . . . . . . add 2y

Substituting for x in the first equation gives ...

  -5(2y +4) +y = -2 . . . . substitute for x

  -9y -20 = -2 . . . . . . . simplify

  -9y = 18 . . . . . . . . .  add 20

  y = -2 . . . . . . . . . . . divide by -9

  x = 2(-2) +4 = 0 . . . . find x using the expression for substitution

The solution is (x, y) = (0, -2).

_____

<em>Additional comment</em>

In some cases, there are no variables that have a coefficient of ±1, so you just need to "bite the bullet" and deal with the resulting fractions.

<u>Example</u>:

  solve for y: -5x +2y = -2

     2y = 5x -2

     y = 5/2x -1 . . . . expression used to substitute for y

Of course, you can multiply the equation after substitution by 2 to eliminate fractions, or just work the problem as is. The point of looking for coefficients of ±1 is to avoid having to do arithmetic with fractions. It can help avoid errors to work with integers, but ultimately the method is the same regardless of the form of the numbers.

__

You don't always have to substitute for the "bare" variable. Sometimes it can save steps to substitute for expressions instead of variables. If our system of equations were ...

  • -5x +2y = -2
  • -3x +6y = -12

You can substitute into the second equation for (2y). In that case, the second equation becomes ...

  -3x +3(2y) = -12

  -3x +3(5x-2) = -12 . . . . . . where 2y = 5x -2

You might be interested in
Two of the Boy Scouts (exercise 19), Tom and Jerry, are weightlifters. They carry 50 lb. per trip. How many trips will each scou
steposvetlana [31]

Answer:

is the the whole question ?

3 0
3 years ago
Find the solution to the system of equations by using a graphing calculator. Describe the steps you took to enter the informatio
Luden [163]

Answer:B.

Step-by-step explanation: I took the same class

3 0
3 years ago
Read 2 more answers
How do I do this problem? I have no idea . Thanks
Ostrovityanka [42]

Answer:

nooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

Step-by-step explanation:

3 0
3 years ago
Solve.<br><br> 5=1/5x−3<br><br> Enter your answer in the box.<br><br> x =
FrozenT [24]
You must multiply 5x-3 with 5, then you will get

25x-15 = 1
25x = 1+15
25x = 16
x = \frac{16}{25}
x = 0.64
3 0
3 years ago
Read 2 more answers
A submarine started the day at 1200 feet below sea level. The submarine rose 60 feet per hour during a 3-hour
Blababa [14]

Answer:

1,200 +3(60)

Step-by-step explanation:

1200 is where they started so every three hour period the submarine rises 60 ft per hour. So you multiply it by this and then 60. Positive because you are rising, and not going down.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Simplify <br>-27z^5 +(-26z^5)​
    12·1 answer
  • In order to solve the equation -3x-6=5, the first step is to
    15·1 answer
  • The <br> 180<br> falls between which two whole numbers?
    5·2 answers
  • A wire is in the shape of a square of side 22 cm. If it is rebent into a circle, then find its radius.
    6·1 answer
  • there are 481 students hiking at black mountain trail. There are 24 adults, and each adult is assigned the same number of studen
    11·1 answer
  • What is the quotient and remainder for 52 divided by 8
    15·1 answer
  • #1: Jim, Jane, Ann, and Bill measure an object’s length, density, mass, and volume, respectively. Which student’s measurement mi
    11·2 answers
  • Fatima Sheroud sells children's clothing for The
    14·1 answer
  • What is 20% off of 113.83?
    7·2 answers
  • Pls hurry and no links
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!