Page 16 - 10th maths -1

Let’s learn.

Graphical method

Ex. Let’s draw graphs of x + y = 4, 2x - y = 2 and observe them.

x + y = 4 2x - y = 2
x -1 4 1 6 x 0 1 3 -1

y 5 0 3 -2 y -2 0 4 -4

(x, y) (-1, 5) (4, 0) (1, 3) (6,-2) (x, y) (0, -2) (1, 0) (3, 4) (-1,-4)

Y Scale Each point on the graph
on both axes
(-1,5) 5 y = 2 1 cm = 1 Unit satisfies the equation. The

4 (3,4) two lines intersect each
other at (2, 2).
(1,3) 2x -
3 Hence ordered pair (2, 2)
i.e. x = 2, y = 2 satisfies
2 (2,2)
the equations x + y = 4
1
and 2x - y = 2.
(1,0) (4,0) The values of variables that
X' -2 -1 0 1 2 3 4 5 6 X
satisfy the given equations,
-1
give the solution of given
(6,-2)
-2 (0,-2) equations.
x +
\ the solution of given
-3
y = 4
equations x + y = 4,
(-1,-4) -4 2x - y = 2 is x = 2,

-5 y = 2.
Y'

Let’s solve these equations by method of elimination.
x + y = 4 . . . (I) substituting this value in equation (I)

2x - y = 2 . . . (II) x + y = 4
Adding equations (I) and (II) we \ 2 + y = 4

get, \ y = 2
3x = 6 \ x = 2

7