Question

How many solutions does this linear system have?

y = 2x – 5

–8x – 4y = –20

Answer 1

Hello,

One solution (5/2,0)

since
y=2x-5==>2x-y=5 (1)
-8x-4y=-20==>2x+y=5(2)
(1)+(2)==>4x=10==>x=5/2
y=2*5/2-5==>y=0

Answer 2

Answer:

Given linear system of equation has only 1 solution.

Step-by-step explanation:

Given System of linear equation is,

y = 2x - 5

-8x - 4y = -20

rewriting the given system in standard form,

2x - y - 5 = 0

-8x - 4y + 20 = 0

We know that number of solution of the system of equation is determined by comparing the ratios of coefficient and constant term.

here coefficient of x that is $a_1=2\:,\:a_2=-8$

coefficient of y that is $b_1=-1\:,\:b_2=-4$

constant term that is $c_1=-5\:,\:c_2=20$

we have,

$\frac{a_1}{a_2}=\frac{2}{-8}=\frac{-1}{4}\:\:,\:\:\frac{b_1}{b_2}=\frac{-1}{-4}=\frac{1}{4}\:\:and\:\:\frac{c_1}{c_2}=\frac{-5}{20}=\frac{-1}{4}$

Since, $\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$

We only have one unique solution.

Therefore, Given linear system of equation has only 1 solution.