Solve the system of equations algebraically.
3x-3y=6
6x-7y=8

a.(5,5)
b. many solutions
c. no solution
d. (6,4)

The correct option is d.

Step-by-step explanation:

The given equations are

              ....(1)

               ..... (2)

Multiply equation (1) by  by 2, to make same coefficient of x.

              ....(3)

Subtract equation (2) form equation (3).

Substitute this value in equation (1),

The solution of the given system of equation is (6,4).

Therefore the correct option is d.

Choice d is correct answer.

Step-by-step explanation:

We have given two equation.

3x-3y = 6                eq(1)

6x-7y = 8                eq(2)

We have to find the solution of given equations.

Multiplying by both sides of eq(1) by 2, we have

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

6x-6y = 12                  eq(3)

Subtracting eq(3) to eq(2) , we have

6x-6y -(6x-7y) = 12-8

6x-6y-6x+7y = 4

Adding like terms, we have

6x-6x+7y-6y = 4

y = 4

Putting the value of y in eq(1), we have

3x-3(4) = 6

3x-12 = 6

Adding 12 to both sides of above equation, we have

3x-12+12= 6+12

3x = 18

Dividing by 3 to both sides of above equation , we have

3x/3 = 18/3

x = 6

Hence, the solution set is (6,4).

ok

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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