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Linear Equations

Math 0097  Linear Equations: Finding X and Y Intercepts


 

 

1. Solve the following systems by substitution

X + Y = 6

Y = 2x

 

2. The sum of two numbers is 140 and their difference is 20.  Find the numbers.

 

 

3. In which quadrant does the point (-3, 5) lie?

A. QI
B. QII
C. Q III
D. QIV
E. x-axis

 

4.  Find the slope of the line through the following pairs of points: (-3,2), (3,-2)

 

 

5. Find the slope of the line given pair of points: (2,3), (3,5)

 

 

6. Solve the following system by graphing:

X – 2Y = -4

Y = – X – 1

 

 

7. Solve the following system:

2X + Y =2

X   – 3Y= 29

 

8. The sum of two numbers is 112 and their difference is 20.  Find the numbers.

 

 

9.  Find the x- and y- intercepts: 3x – 4y = – 12

 

 

10.  Find the equation of the line with the given slope and y-intercept

m=-4, b=0

 

11. Complete the ordered pairs for the equation 3x + 6y = 12 and label the x-intercept and the y-intercept.

(0,       )            (            , 0)                  (10,           )

 

12. By writing the word “yes” or “no”  in the blank indicate which of the following ordered pairs are solutions to the equation 4x + 2y = 16?

_____ (4, 0)     _____(0, 8)              _____ (-5, -2)            _____ (3, 4)

 

13. Find the x-intercept and the y-intercept: y = -4x – 16

 

 

14. Graph and label: y = -2 and x = 3.  Your graph will have a horizontal line and a vertical line.

What is the point of intersection?  ______

 

 

 

15. Solve this system by graphing:

X +Y = 5

X-Y=  3

 

 

16. Find the x-intercept and the y-intercept: y = -8x – 40             

 

 

17. Find the x-intercept and the y-intercept: 10x – 6y = 30

 

 

18. Solve this system by graphing.

X + Y = 2

X – Y = -6

 

 

19. Solve this system by graphing.

X + 3Y = 12

Y = 2/3 X -2

 

 

20. Solve this system using the addition method.

X + 3Y = 8

-X + 4Y = 6

 

21. Solve this system using the addition method.

-2X + 5Y = 11

3X + Y = 9

 

22. Solve this system using the substitution method.

5X – Y = 6

Y = 3X -2

 

23. Solve this system using the substitution method.

2X + 2Y = 14

-2X + Y = 1

 

24.  Tickets for a movie cost $7 for adults and $5 for children.  One afternoon 60 people bought tickets and ticket sales totaled $380.  How many adult tickets were sold?

 

 

25. Adam has 26 coins whose value is $4.40.  If he has only dimes and quarters, how many of each kind of coin does he have?

 

 

26. Find the x- and y- intercepts: y = 5x – 10

a) x-intercept 5, y-intercept -10

b) x-intercept -2, y-intercept -10

c) x-intercept -5, y-intercept -10

d) x-intercept 2, y-intercept -10

 

27. Find the x- and y- intercepts: 3x – 5y =  -15

a) x-intercept 5, y-intercept 3

b) x-intercept -5, y-intercept 3

c) x-intercept 5, y-intercept -3

d) x-intercept -5, y-intercept -3

 

28. Solve the system:

3X + 2Y = 12

-2X + Y = -1

 

29. Solve the system:

X + 2Y = 1

3X – Y = 24

 

30. The sum of two numbers is 120 and their difference is 80.  Find the numbers.

 

 

 

 

Answers

  1. (2, 4)
  2. The two numbers are 80 and 60.
  3. B
  4. -2/3
  5. 2
  6. (-2, 1)
  7. (5, -8 )
  8. 66 and 46
  9. x-intercept -4, y-intercept 3
  10. Y = =-4x
  11. (0, 2) y-intercept, (4, 0) x-intercept, (10, -3)
  12.  yes, yes, no, no
  13. (0, -16) is y-intercept, (-4,0) x-intercept
  14.  (3,-2)
  15. (4, 1)
  16.  y-int (0,-40), x-int (-5,0)
  17.  y-int (0,-5), x-int (3,0)
  18.  (-2,4)
  19.  (6,2)
  20.  (2,2)
  21.  (2,3)
  22.  (2,4)
  23.  (2,5)
  24.  40
  25.  14 dimes, 12 quarters
  26.  d
  27.  b
  28.  (2, 3)
  29.  (7,-3) 
  30.  100 and 20