Question

How many solutions does this linear system have? y=2x-5, -8x-4y=-20

Answer 1

-8x-4y=-20
-2x-y=-5
y=-2x+5

1 solutions
2x-5=-2x+5
4x=10
X=2.5

Answer 2

Answer: There is only one solution.

Explanation:

Since we have given that

`y=2x-5\\\\\implies 2x-y=5---------(1)\\\\-8x-4y=-20\\\\\implies 2x+y=5---------(2)`

We will check its consistency and type of line:

From eq(1)

`a_1=2\\\\b_1=-1\\\\c_1=5`

From eq(2)

`a_2=2\\\\b_2=1\\\\c_2=5`

So, it becomes,

`(a_2)/(a_1)=(b_2)/(b_1)\\\\(2)/(2)=(1)/(-1)\\\\1\\eq -1`

So, it is an intersecting line which has unique solution.

Hence, there is only one solution.