Question

How many solutions does this linear system have? y = 2x – 5 –8x – 4y = –20 one solution: (–2.5, 0) one solution: (2.5, 0) no solution infinite number of solution

Answer 1

one solution: (2.5, 0)

Explanation:

We are given the following system of equations:

y = 2x - 5

-8x - 4y = -20

Replacing the first equation into the second:

`-8x - 4(2x - 5) = -20`

`-8x -8x + 20 = -20`

`-16x = -40`

`16x = 40`

`x = (40)/(16)`

`x = 2.5`

y

`y = 2x - 5 = 2(2.5) - 5 = 5 - 5 = 0`

Thus the system has one solution: (2.5,0).