In this method the coefficients of either x or y are made same by multiplying with a suitable number. Then the sign of the equalled coefficients are observed. If the sign of the equalled coefficients are same then both the equations are subtracted and if the sign of both the equalled coefficients are different then both the equations are added.

After performing addition or subtraction, one coefficient, either x or y is eliminated and value of the same coefficient is obtained. The value of the obtained coefficient is then put into any of the given equations and the value of the remaining coefficient is determined.

In this way, the linear equations in two variables are solved using elimination method.

Practice Set 1.1
(1) Complete the following activity to solve the simultaneous equations. 5x + 3y = 9 —–(I)
2x – 3y = 12 —– (II)
Let’s add eqations (I) and (II).
+5x + 3y = 9 2x – 3y = 12
x=
x= x=
Place x = 3 in equation (I).
\ Solution is (x, y) = ( 4
,
5 ́
3y = 9 – 3y =
y= y=
+ 3y = 9
).
32. Solve the following simultaneous equations.
(1) 3a + 5b = 26; a + 5b = 22 (3) 2x – 3y = 9; 2x + y = 13 (5) 5x + 2y = -3; x + 5y = 4
(7) 99x + 101y = 499; 101x + 99y = 501 (8) 49x – 57y = 172; 57x – 49y = 252