SIMULTANEOUS EQUATIONS-1

Solve the following equations by substitution method.

2x - y = 5

x + 3y = 27

Solution

2x - y = 5 ----------- (i)

x + 3y = 27 ---------- (ii)

From equation (i)

2x - y = 5

2x - 5 = y

∴ y = 2x - 5 ----------(iii)

substitute equation (iii) in (ii) above,

x + 3(2x – 5 ) = 27

x + 6x – 15  = 27

x  + 6x  = 27 + 15

 7x  = 42                   [since x+6x=7x and 27+15=42]

7x  = 42

                  

7x = 42

7      7

x = 6

From equation (iii)

y = 2x - 5 ----------(iii)

y = 2(6) – 5

y = 12 – 5

y = 7

Hence x=6 and y=7.

TRY THIS………………………..

Solve the following equations by substitution method.

x + y = 18

2x - y = 14