# Solving Systems of Equations

1. y-2x=0

y=8x-9

What is the solution of the system of equations?

(i need graph also)

2. r-6s=0

9r-8s=230

What is the solution of the system?

3. x+y= -13

9x+y= -61

What is the solution of the system?

4. (1,2); 6x-5y= -4

2x-7y= -12

is the given ordered pair a solution of the system?

yes or no

5. 5x+8y= 27

8x-8y= -144

what is the solution of the system?

6. 9x+6y= 15

-7+y= 28

what is the solution of the system?

7. x+y= 9

y=x+1

what is the solution of the system?

8. 1/2 x + 2/3 y = 2/3

2/3 x - 3/5 y = 1/5

what is the solution of the system?

9. (5,4) 7x-4y= 19

8x-5y= 20

is the given ordered pair a solution of the system?

yes or no

10. x+y= 11

9x-y= 69

what is the solution of the system?

11. p=38+q

9p= -4q+381

what is the solution of the system?

12. 3x-y= 3

4x+y= 4

what is the solution of the system of equations?

(need graph also)

13. 3r-7s= -48

7r+3s= 62

what is the solution of the system?

14. x+y= -2

x-y= 6

what is the solution of the system?

15. x-y= -12

2x-9y= -66

what is the solution of the system?

16. x-y= 15

x+y= 3

what is the solution of the system?

#### Solution Preview

1. y-2x=0

y=8x-9

Then (8x-9) - 2x = 0, then 8x - 9 - 2x = 0, then 6x - 9 = 0, then x = 3/2

So y = 8x - 9 = 3

The solution is x = 3/2 and y = 3, or (3/2, 3)

The graph is attached.

2. r-6s=0 (1)

9r-8s=230 (2)

From (1), we get r = 6s, then we put in (2) and have

9(6s) - 8s = 230, then 54s - 8s = 230, then 46s = 230, then s = 5

so r = 6s = 30

The solution is r = 30, s = 5.

3. x+y= -13 (1)

9x+y= -61 (2)

(2)-(1), then get 8x = -61+13 = -48, then x = -6. Since x + y = -13, then y = -x - 13 = -7.

The solution is x = -6, y = -7, or (-6, -7)

4. (1,2); 6x-5y= -4

2x-7y= -12

is the given ordered pair a solution of the system?

YES

5. 5x+8y= 27 (1)

8x-8y= -144 (2)

(1)+(2) and get 13x = -144 + 27 ...

#### Solution Summary

Systems of equations are solved.