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]
3 years ago
12

Solving systems by substitution

Mathematics
1 answer:
Kipish [7]3 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
What does x equal in 5x+y=-24
qaws [65]

Answer

24/5

Step-by-step explanation:

5 0
4 years ago
Read 2 more answers
Complete factorization for -20x - 5y
marusya05 [52]

Answer:

-5 (4x+y)

Step-by-step explanation:

Factor out -5, and -20/-5=4, -5/-5=1.

7 0
3 years ago
Find the lower quartile of this data set: 593, 588, 540, 434, 420, 398, 390, 375
Sergio [31]
Happy birthday wooooo
5 0
3 years ago
Read 2 more answers
Monet began heating a solution with a starting temperature of 67°F. The temperature increased by 3° per minute.
STALIN [3.7K]

Answer:

46

Step-by-step explanation:

6 0
3 years ago
A line passes through the point (4,–2) and is perpendicular to the line with the equation y = 2∕3x + 4. What's the equation of t
prisoha [69]

Answer:

Step-by-step explanation:

perp. -3/2

y + 2 = -3/2(x - 4)

y + 2 = -3/2x + 6

y = -3/2x + 4

answer is D

5 0
3 years ago
Other questions:
  • Suppose the researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to a
    8·1 answer
  • The outdoor temperature yesterday reached a low of -4.5 degrees Farenheit. Between what two intergers was the temperature?
    12·2 answers
  • Do integers have to be a set of positive and negative numbers?
    13·1 answer
  • If the squared difference of the zeroes of the quadratic polynomial x2+kx+30 is equal to 169 find the value of k and the zeroes
    10·1 answer
  • What is the additive inverse of non complex 9
    7·1 answer
  • ABCD is a rectangle. MBCE = 4x-23 and mDCE = 5+5x.
    5·1 answer
  • Find the value of x<br>answer options <br>9,15,10,14​
    10·1 answer
  • What algebraic property is T - 6 = -4
    5·2 answers
  • A procedure has an 81% success rate. The procedure is tried on 12 patients what is the probability that at least 8 patients show
    11·1 answer
  • Emily bought four boxes. A week later
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!