Solve equations by substitution

Question

2x+4y=10

5x−3y=11

Answer 1

The simultaneous equations are

2x + 4y  =  10 -------------> (1)

5x − 3y  =  11 --------------> (2)

From the equation (1)

2(x + 2y)  =  10

x + 2y  =  10/2

x + 2y  =  5

x  =  5 - 2y -----------------> (3)

Substitute x  =  5 - 2y in Eq (2)

5(5 - 2y) − 3y  =  11

25 - 10y − 3y  =  11

25 - 13y  =  11

25 - 11  =  13y

13y  =  14

y  =  14/13

Substitute y = 14/13 in Eq (3)

x  =  5 - 2(14/13)

x  =  5 - 28/13

x  =  (65 - 28)/13

x  =  37/13

Answer :

The Solutions are x  =  37/13  and  y = 14/13.