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, \(\frac{a_1}{a_2}
eq\frac{b_1}{b_2}\)
We only have one unique solution.
Therefore, Given linear system of equation has only 1 solution.
