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
ad-work [718]
2 years ago
7

Solve the following systems of equations by substitution method.

Mathematics
2 answers:
kupik [55]2 years ago
7 0

Answer:

See below for all answers and explanations

Step-by-step explanation:

<u>Problem 1</u>

4x - 3y = 18

4x - 3(-2) = 18 <-- Substituting y = -2

4x + 6 = 18

4x = 12

x = 3

<u>Problem 2</u>

2x + 3y = 7

2x + 3(6x-11) = 7 <-- Substituting y = 6x - 11

2x + 18x - 33 = 7

20x - 33 = 7

20x = 40

x = 2

y = 6x - 11 <-- Substituting x=2 to solve for y

y = 6(2) - 11

y = 12 - 11

y = 1

<u>Problem 3</u>

4x - 5y = -3

4(-3y-5) - 5y = -3 <-- Substituting x = -3y - 5

-12y - 20 - 5y = -3

-17y - 20 = -3

-17y = 17

y = -1

x = -3y - 5 <-- Substituting y = -1 to solve for x

x = -3(-1) - 5

x = 3 - 5

x = -2

<u>Problem 4</u>

-2x - 3y = -12

-2(5y-7) - 3y = -12 <-- Substituting x = 5y - 7

-10y + 14 - 3y = -12

-13y + 14 = -12

-13y = -26

y = 2

x = 5y - 7 <-- Substituting y=2 to solve for x

x = 5(2) - 7

x = 10 - 7

x = 3

<u>Problem 5</u>

5x - 3y - 8 = 2x - 3y - 6 <-- Setting equations equal to each other

5x - 8 = 2x - 6 <-- Eliminating y-variable to solve for x

3x - 8 = -6

3x = 2

x = 2/3

5x - 3y - 8 = 0 <-- Substituting x = 2/3 into first equation

5(2/3) - 3y - 8 = 0

10/3 - 3y - 8 = 0

10/3 - 3y - 24/3 = 0

-14/3 - 3y = 0

-3y = 14/3

y = -14/9

<u>Problem 6</u>

x - 3y - 11 = 0 <-- Solve for x

x - 3y = 11

x = 11 + 3y

5x + y - 7 = 0

5(11+3y) + y - 7 = 0 <-- Substituting x = 11 + 3y

55 + 15y + y - 7 = 0

55 + 16y - 7 = 0

48 + 16y = 0

16y = -48

y = -3

x = 11 + 3y <-- Substitute y=-3 into first equation to solve for x

x = 11 + 3(-3)

x = 11 - 9

x = 2

<u>Problem 7</u>

2x - 3y = - 1

2x - 3(x-1) = -1 <-- Substituting y = x - 1

2x - 3x + 3 = -1

-x + 3 = -1

-x = -4

x = 4

y = x - 1 <-- Substitute x=4 to solve for y

y = 4 - 1

y = 3

<u>Problem 8</u>

-4x + y = 6 <-- Solve for y in first equation

y = 6 + 4x

-5x - y = 21

-5x - (6+4x) = 21 <-- Substituting y = 6 + 4x

-5x - 6 - 4x = 21

-9x - 6 = 21

-9x = 27

x = -3

y = 6 + 4x <-- Substitute x = -3 to solve for y

y = 6 + 4(-3)

y = 6 - 12

y = -6

Anuta_ua [19.1K]2 years ago
6 0

Answer:

1) x = 3 and y = -2

2) x = 2 and y = 1

3) x = -2 and y = -1

4) x = 3 and y = 2

5) x = 2

6) x = 2 and y = -3

7) x = 4 and y = 3

8) x = -3 and y = -6

Step-by-step explanation:

1. Answer :

y = -2

4x - 3y = 18 ----(1)

Substitute y = -2 in (1).

4x - 3(-2) = 18

4x + 6 = 18

Subtract 6 from both sides.

4x = 12

Divide both sides by 4.

x = 3

So,

x = 3 and y = -2

2. Answer :

y = 6x - 11 ----(1)

2x + 3y = 7 ----(2)

Substitute y = 6x - 11 in (2).

2x + 3(6x - 11) = 7

2x + 18x - 33 = 7

20x - 33 = 7

Add 33 to both sides.

20x = 40

Divide both sides by 20.

x = 2

Substitute x = 2 in (1).

y = 6(2) - 11

= 12 - 11

= 1

So,

x = 2 and y = 1

3. Answer :

x = -3y - 5 ----(1)

4x - 5y = -3 ----(2)

Substitute x = -3y + 5 in (2).

4(-3y - 5) - 5y = -3

-12y - 20 - 5y = -3

-17y - 20 = -3

Add 20 to both sides.

17y = -17

Divide both sides by 17.

y = -1

Substitute y = -1 in (1).

x = -3(-1) - 5

= 3 - 5

= -2

So,

x = -2 and y = -1

4. Answer :

x = 5y - 7 ----(1)

-2x - 3y = -12 ----(2)

Substitute x = 5y - 7 in (2).

-2(5y - 7) - 3y = -12

-10y + 14 - 3y = -12

-13y + 14 = -12

Subtract 14 from both sides.

-13y = -26

Divide both sides by -13.

y = 2

Substitute y = 2 in (1).

x = 5(2) - 7

= 10 - 7

= 3

So,

x = 3 and y = 2

5. Answer :

5x + 3y - 8 = 0 ----(1)

2x - 3y - 6 = 0 ----(2)

Solve for 3y in (1).

5x + 3y - 8 = 0

Subtract 5x from both sides.

3y - 8 = -5x

Add 8 to both sides.

3y = -5x + 8

Substitute 3y = -5x + 8 in (2).

2x - (-5x + 8) - 6 = 0

2x + 5x - 8 - 6 = 0

7x - 14 = 0

Add 14 to both sides.

7x = 14

Divide both sides by 7.

x = 2

6. Answer :

x - 3y - 11 = 0 ----(1)

5x + y - 7 = 0 ----(2)

Solve for x in (1).

x - 3y - 11 = 0

Subtract 3y and 11 to both sides.

x = 3y + 11 ----(3)

Substitute x = 3y + 11 in (2).

5(3y + 11) + y - 7 = 0

15y + 55 + y - 7 = 0

16y + 48 = 0

Subtract 48 from both sides.

16y = -48

Divide both sides by 16.

y = -3

Substitute y = -3 in (3).

x = 3(-3) + 11

= -9 + 11

= 2

So,

x = 2 and y = -3

7. Answer :

2x - 3y = -1 ----(1)

y = x - 1 ----(2)

Substitute y = x - 1 in (1).

2x - 3(x - 1) = -1

2x - 3x + 3 = -1

-x + 3 = -1

Subtract 3 from both sides.

-x = -4

Multiply both sides by -1.

x = 4

Substitute x = x in (3).

y = 4 - 1

= 3

So,

x = 4 and y = 3

8. Answer :

-4x + y = 6 ----(1)

-5x - y = 21 ----(2)

Solve for y in (1).

-4x + y = 6

Add 4x to both sides.

y = 4x + 6 ----(3)

Substitute y = 4x + 6 in (2).

-5x - (4x + 6) = 21

-5x - 4x - 6 = 21

-9x - 6 = 21

Add 6 to both sides.

-9x = 27

Divide both sides by -9.

x = -3

Substitute x = -3 in (3).

y = 4(-3) + 6

= -12 + 6

= -6

So,

x = -3 and y = -6

Learn more:

brainly.com/question/26555025

Social studies

brainly.com/question/26539371

Mathematics

brainly.com/question/26537282

Divisibility - Math

brainly.com/question/26525264

Mathematics

Thank You!

Answered by: ms115

You might be interested in
(3x/2)^4 any answers
Anika [276]

\bf \left( \cfrac{3x}{2} \right)^4\implies \left( \cfrac{(3x)^4}{2^4} \right)\implies \left( \cfrac{3^4x^4}{2^4} \right)\implies \cfrac{81x^4}{16}

6 0
3 years ago
Read 2 more answers
I WILL AWARD BRAINLIEST!
gavmur [86]

Answer:

A. 70

Step-by-step explanation:

You can use the transversals and use vertical angles are congruent.

7 0
3 years ago
Read 2 more answers
Find all the missing measurement​
Allushta [10]
H 32 and k is 50 this is right because I had this and passed.
6 0
2 years ago
A student has gotten the following grades on his tests. What is the minimum grade he must get on the last test in order to have
steposvetlana [31]
In order to get an 81 average, 
the student has to get 81x5=405

71+96+90+73+?=405
330+?=405
405-330=75
he needs to get an 75

3 0
3 years ago
Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?
Paha777 [63]

Answer:

the second one

Step-by-step explanation:

trust me i've done this before

5 0
2 years ago
Other questions:
  • To the nearest tenth, what is the area of the shaded segment when AG = 6 ft?
    10·2 answers
  • Picture picture picture
    11·2 answers
  • In the class , 0.48 of the students have brown hair. 3/11 of the students have blonde hair . What percent of students have neith
    15·1 answer
  • 9) Gusnie uses
    12·1 answer
  • What is the value of 2 b + 24 equals 30​
    13·2 answers
  • What is the solution?<br> -10 = 2a – 4
    11·2 answers
  • A sequence is defined by the function f ( n ) = f ( n − 1 ) + 5 , where n represents the number of the term for n &gt; 1 , and f
    8·1 answer
  • In 4th grade :) help plss
    6·2 answers
  • (-5)^-4 Write it as a positive exponent
    14·2 answers
  • How do you solve this?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!