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Applied Finite Mathematics HW Solutions 11

Applied Finite Mathematics HW Solutions 11 - EXERCISES 1.3...

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Unformatted text preview: EXERCISES 1.3 _ 9 16. To find the s~coordinate where the line a: + 2y = 4 intersects the line y = 1, we solve :1: + 2(1) = 4 => 3 = 2. The point of intersection is therefore (2,1). The equation of the required line is —1=—2(:1:—2) =5 y—1=-2m_+4 =5 2:1:+y=5. (b)-ln slope y-intercept form the equation is y = —2:1: + 5. 17. To find the point where the line a: + 2y: 4 cuts the y-axis we set :1:: 0 in the equation of the line, 2y = 4 z; y = 2. The point is therefore (0, 2). To find the point where the line :1: — 4y = 5 intersects the line 3; = -— 1, we solve —1)=—5 => 111:1. The point is (1, -—1). Using these two points, the slope of the required line is ——l —2 . , . . m = 1 _ 0 = —-3. The equat1on of the reqrnred hue Is y—2=—-3(a:~0) =>3m+y=2. - 18. To find the point of intersection, we solve the first equation for :1: in terms of 3;, getting :1: = 2 -— 23;. When we substitute this into the second equation, we obtain 5(2—2y)+2y=10 => 10—10y+2y=10 =‘> —8y=10-—1o=o' = yes. This implies that the :1:-coordinate of the point of intersection is a: = 2 — 2(0) = 2. The point of intersection is (2,0). The lines and point of intersection are shown in the left figure below. 19. To find the point of intersection we solve the first equation for :1: in terms of 3;, getting :1:-— —1 2y— 2. When we substitute this into the second equation, we obtain » 2(2y—2)—-5y =—10 => 4y-— 4— 5y=—10 => --y=—.10+4=—6 =1. y=6. This implies that the m-coordinate of the point of intersection is a: = 2(6) — 2 = 10. The point of intersection is (10,6). The lines and point of intersection are shown in the right figure above. 20. To find the point of hitersection, we solve the first equation for a: in terms of y, getting :1: z 5 — y. When we substitute this into the second equation, we obtain . 3 3(5-y)+y=12 —‘——> 15—3y+y=12 —‘——> —2y=12—-15=—3 => y=§. This implies that the m—coordinate of the point of intersection is m 2 5— 3/2— — 7/2. The point of intersection is (7/2, 3/2). The lines and point of intersection are shown in the left figure below. Thismaicrial'hes beenr'eprochced inam’danoowim oopyrigln law hythe University ofManitoha Bookstore. Further mailmm in “-1.1 m- an a." 1.. ...:...1.. —--'-!I-=--I ...
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