Question

Solve the following simultaneous equations graphically
(1) x + y = 6 ; x - y = 4
(2) x + y = 5; x - y = 3
(3) x + y = 0; 2x - y = 9
(4) 3x - y = 2 ; 2x - y = 3
(5) 3x - 4y = - 7 ; 5x – 2y = 0
(6) 2x - 3y = 4 ; 3y - x = 4​

Answer 1

Answer:

i. The given simultaneous equations are

x + y = 6

∴ y = 6 - x

x 0 6 3 4

y 6 0 3 2

(x,y) (0,6) (6,0) (3,3) (4,2)

x - y = 4

∴ y = x - 4

x 0 4 2 5

y -4 0 -2 1

(x,y) (0,-4) (4,0) (2,-2 (5,1)

The two lines intersect at point (5, 1).∴ x = 5 and y = 1 is the solution of the simultaneous equations x+ y = 6 and x – y = 4.

ii. The given simultaneous equations are

x + y = 5

∴ y = 5 - x

x 0 5 2 3

y 5 0 3 2

(x,y) (0,5) (5,0) (2,3) (3,2)

x - y = 3

∴ y = x - 3

x 0 3 2 1

y -3 0 -1 -2

(x,y) (0,-3) (3,0) (2,-1) (1,-2)

The two lines intersect at point (4, 1).

∴ x = 4 and y = 1 is the solution of the simultaneous equations x+y = 5 and x – y = 3.

iii. The given simultaneous equations are

x + y = 0

∴ y = - x

x 0 2 -2 -1

y 0 -2 2 1

(x,y) (0,0) (2,-2) (-2,2) (-1,1)

2x - y = 9

∴ y = 2x - 9

x 0 2 5 4

y -9 -5 1 -1

(x,y) (0,-9) (2,-5) (5,1) (4,-1)

The two lines intersect at point (3, -3).

∴ x = 3 and y = -3 is the solution of the simultaneous equations x + y = 0 and 2x – y = 9.

Answer 2

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