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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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