Question

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

Answer 1

Answer: There is only one solution.

Step-by-step 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,

$\frac{a_2}{a_1}=\frac{b_2}{b_1}\\\\\frac{2}{2}=\frac{1}{-1}\\\\1\neq -1$

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

Hence, there is only one solution.

Answer 2

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

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