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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.

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