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Graphically Solved algebra problems

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Question 21

Question: Solve graphically:
3x + y + 1 = 0 and 2x - 3y + 8 = 0.

Answer: a) 3x + y + 1 = 0
y = -3x - 1

b) 2x - 3y + 8 = 0
3y = 2x + 8

Question 22

Question: Find graphically, the vertices of the triangle whose sides are y = x + 5, y = -x and x = 3. Also find the area of the triangle.

Answer: a) y = x + 5

b) y = -x

c) x = 3
Vertices of D ABC are:
A (-2.5, 2.5)
B (3, 8)
C (+3, -3)

Question 23

Question: Solve graphically
y = 2x - 6 and y = -2x + 10.

Answer: a) y = 2x - 6

b) y = -2x + 10

Question 24

Question: Solve graphically the vertices of the triangle of sides 2y + x = 0, 3y = x and x = 6. Also find area of the triangle.

Answer: a) 2y + x = 0

2y = -x

b) 3y = x

c) x = 6
Vertices of DABC are:
A (0,0), B (6,2), C (6,-3)

Question 25

Question: Solve graphically:
3y = 5 - x and 2x = y + 3.

Answer: 1) 3y = 5 - x

2) 2x = y + 3
y = 2x - 3

Question 26

Question: Solve graphically:
x + y = -1 and y - 2x = -4.

Answer: a) x + y = -1
y = -x -1

b) y - 2 x = -4
y = 2x - 4

Question 27

Question: Which of the following equations have x=2, y=3 as solution ?
(a) 2x+3y=8 (b) x-2y = -4 (c) 5x-2y = 4

Answer: (a) Substitute x=2, y=3 in 2x+3y=8
2(2)+3(3)=8

x = 2, y = 3 is not a solution .
(b) Substitute x=2, y=3 in x-2y=-4

(c) Substitute x=2m y=3 in 5x-2y=4

4=4
x=2, y=3 is a solution of 5x-2y=4

Question 28

Question: Find atleast 3 solutions of :
(a) 2x+4y=12 (b) 3x+5y=10 (c) x+3y=6 (d) 2x-5y=8

Answer: (a) 2x+4y=12
2x=12-4y

x=6, y=0; x=2, y=2 and x=+10, y=-2 are three
Solution of 2x+4y=12 .
(b) 3x+5y=10
5y=10-3x

x=0, y=2; x=5, y=-1 and x=-5, y=5 are three solutions of 3x+5y=10
(c) x+3y=6
x=6-3y
Put y=0, x=6
y=1, x=6-3 = 3
y=2, x=6-6 = 0
x=6, y=0; x=3 y=1; x=0, y=2 are solutions of x+3y=6
(d) 2x-5y=8
2x=8+5y

x=4, y=0; x=9, y=2; x=-1, y=-2 are solutions of 2x-5y=8

Question 29

Question: Find the values of a so that x=1, y=2 is a solution of:
(a) 3x-ay=5 (b) ax-5y=17 (c) 3x+2ay=11

Answer: (a) 3x-ay=5
substitute x=1, y=2
3(1)-a(2)=5
3+5=2a

a=4
(b) ax-5y=17
substitute x=1, y=2
a(1)-5(2)=17
a-10 = 17
a = 27
(c) 3x+2ay=11
substitute x=1, y=2
3(1)+2a(2)=11
3+4a=11
4a=11-3
4a=8

a=2