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

Question

asked Apr 13, 2019 229k views

2 Answers

Fehrlich · Answer 1 · 2019-04-20T06:48:59+0000

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.