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: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.