Question

solve the system by substitution 2x+y=10 x-3y=-2 state whether the system had one solution infinite solutions or no solution

Answer 1

System has only one solution. x= 4 and y = 2.

Explanation:

We have given two equations :

2x + y = 10 ----------(1)

x - 3y = -2 ----------(2)

From equation (2), we can write:

x - 3y = -2

or x = -2 + 3y , substitute this in equation (1).

We get, 2x + y = 10

2*(-2 + 3y) + y = 10

-4 + 6y + y = 10

7y = 10 + 4

y = 14/7 = 2

And x = -2 + 3*2 = -2 + 6 = 4

Hence we get x= 4 and y = 2. System has only one solution