Question 1. in the below system, solve for y in the first equation. x + 3y = 6 2x − y = 10 one thirdx + 2 negative one thirdx + 6 −x + 2 negative one thirdx + 2 question 2. what is the value of y in the solution to the following system of equations? 5x − 3y = −3 2x − 6y = −6 −1 0 1 2 question 3. solve 7x − 2y = −3 14x + y = 14 (4, five sevenths) (4, seven fifths) (five sevenths, 4) (seven fifths, 4) question 4. solve x + 3y = 9 3x − 3y = −13 (−1, ten thirds) (1, negative ten thirds) (−1, 3 over 10) (1, negative 3 over 10) question 5. use the substitution method to solve the following system of equations: 4x − y = 3 7x − 9y = −2 (1, 1) (6, −3) (6, 1) (1, −3) question 6. solve 5x − 6y = −38 3x + 4y = 0 (4, 3) (−4, 3) (4, −3) (−4, −3) question 7. solve 2x + 5y = −13 3x − 4y = −8 (4, 1) (−4, 1) (4, −1) (−4, −1)

Answer for Question (1):

The system of equations: x+3y=6

2x-y=10

Solve the first equation x+3y=6 for y:

Subtracting x on both sides,

x+3y-x=6-x

3y=6-x

Now dividing 3 on both sides, we get

y=2-x/3 = negative one third x + 2

Thus y= negative one third of x +2

Answer for question (2):

The system of equation :

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

2x-6y=-6 -->(2)

Multiply equation (1) by 2, we get 10x-6y=6.

Subtracting (1) by (2), we get 8x=0 implies x=0.

Plug in x=0 in equation (1), 0-3y=-3

Dividing -3 on both sides,

y=-3/-3=1

So the solution of y is 1.

Answer for Question (3):

System of equation:

7x-2y=-3 (1)

14x+y=14 (2)

Multiply (2) by 2,

28x+2y=28 (3)

Adding (1) and (3), we get 35x=25

Now dividing 35 on both sides, x=25/35=5/7.

Plug in x=5/7 in equation (1), we get 5-2y=-3

-2y=-3-5

-2y=-8

Dividing -2 on both sides,

y=4

Thus the solution of this system of equation as (5/7,4).

Answer for question (4):

x + 3y = 9 ---> (1)

3x − 3y = −13 ---> (2)

Adding equation (1) and (2), we get

4x=-4

Dividing 4 on both sides,

x=-1

Plug in x=-1 in equation (1), we get

-1+3y=9

Adding 1 on both sides,

3y=9+1=10

Now dividing 3 on both sides,

y=10/3.

so the solution is (-1,10/3).

Answer for question (5):

System of equation is 4x − y = 3 (1)

7x − 9y = −2 (2)

consider the first equation 4x-y=3

Adding y on both sides, 4x=3+y

subtracting 3 on both sides, we get y=4x-3

Substitute y=4x-3 in equation (2),

7x-9(4x-3)=-2

7x-36x+27=-2

Combine the like terms,

-29x+27=2

Adding 27 on both sides,

-29x=-29

dividing -29 on both sides,

x=1

Plug in x=1 in y=4x-3,

y=4(1)-3=1

Then the solution is (1,1).

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation: