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 solutions

Answer 1

The solution is (2.5,0)....

Answer 2

Option 2 - One solution: (2.5, 0)

Explanation:

Given : Two linear equation -

Equation 1 -
`y = 2x - 5`

Equation 2 -
`-8x - 4y = -20`

To find : How many solutions does this linear system have?

Solution :

We solve the given equations,

Substitute the value of y from equation 1 in equation 2

`-8x - 4y = -20`

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

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

`-16x=-40`

`x=(40)/(16)`

`x=2.5`

Now, put value of x in equation 1

`y = 2x - 5`

`y = 2(2.5) - 5`

`y = 5 - 5`

`y = 0`

There is one solution (x,y) = (2.5, 0)

Option 2 is correct.