Solve each system of equations. Write in (x,y) format. 1. 3x+6y=14 2. y=x 3. 7x+

Question

Solve each system of equations. Write in (x,y) format.

1. 3x+6y=14 2. y=x 3. 7x+2y=-8 4. 5x+y=0

   x+2y=3 x-4y=0 8y=4x -5x+2y=30

5. John has a total of nine stamps, which consists of 25-cent and 2-cent stamps. His stamps have a value of $1.10. How many of each stamp does he have.

6. Pump Up Gym has an initial joining fee of $205 and monthly membership dues of $15. Universe Gym has an initial joining fee of $125 and a monthly membership dues of 19$

   When will the costs to join and maintain membership at the gyms be equal.

7. If you planned on continuing you gym membership for only 2 years, which gym would you join? Explain.

Solve each system of inequalities by graphing.

Questions: 1-4, 6, and 8-10 all have multiple choices with them. If you want me to give them to you in a comment just ask if not I really hope you can do all of these. Thanks A BUNCH!!!

Explanation / Answer

FIRST PROBLEM

1. By elimination method, multiply the second equation by -3 to eliminate one of the variables.

3x + 6y = 14
-3(x + 2y = 3)

3x + 6y = 14
-3x - 6y = -9

0x + 0y = 9

Note that any numbers multiplied by 0 always give zero. It's impossible to determine the solution for this system of equations. Hence, the solution does not exist.

SECOND PROBLEM

y = x

x - 4y = 0

Substitute x with y for the second equation and solve for y...

y - 4y = 0

-3y = 0

y = 0

Since x = y = 0, the solution is (0,0).

THIRD PROBLEM

7x + 2y = -8

8y = 4x

For the second equation, divide both sides by 4, which gives us:

2y = x

Substitute x with 2y to the first equation and solve for y...

7(2y) + 2y = -8

14y + 2y = -8

16y = -8

y = -8/16

y = -½

Substitute the value of y to either equation. Let's take the second equation and substitute y with -½.

8(-½) = 4x

-4 = 4x

x = -1

The solution for the system of equations is (-1,-½).

I hope this helps (Sorry that I can't help you solve the fourth problem since it doesn't contain more than one equation.)!

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