# 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**

- (2, 4)
- The two numbers are 80 and 60.
- B
- -2/3
- 2
- (-2, 1)
- (5, -8 )
- 66 and 46
- x-intercept -4, y-intercept 3
- Y = =-4x
- (0, 2) y-intercept, (4, 0) x-intercept, (10, -3)
- yes, yes, no, no
- (0, -16) is y-intercept, (-4,0) x-intercept
- (3,-2)
- (4, 1)
- y-int (0,-40), x-int (-5,0)
- y-int (0,-5), x-int (3,0)
- (-2,4)
- (6,2)
- (2,2)
- (2,3)
- (2,4)
- (2,5)
- 40
- 14 dimes, 12 quarters
- d
- b
- (2, 3)
- (7,-3)
- 100 and 20