Respuesta :
Answer:
[tex]\dfrac{a}{b}=0.75[/tex].
Step-by-step explanation:
If two equations [tex]a_1x+b_1y+c_1=0[/tex] and [tex]a_2x+b_2y+c_2=0[/tex] has infinitely many solutions, then
[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]
The given equations are
[tex]ax+by=10[/tex]
[tex]3x+4y=20[/tex]
It is given that the above system of equations has infinitely many solutions. So,
[tex]\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{10}{20}[/tex]
[tex]\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{1}{2}[/tex]
Now,
[tex]\dfrac{a}{3}=\dfrac{1}{2}[/tex] and [tex]\dfrac{b}{4}=\dfrac{1}{2}[/tex]
[tex]a=\dfrac{3}{2}[/tex] and [tex]b=\dfrac{4}{2}[/tex]
[tex]a=1.5[/tex] and [tex]b=2[/tex]
So, a=1.5 and b=2.
Now,
[tex]\dfrac{a}{b}=\dfrac{1.5}{2}=0.75[/tex]
Therefore, [tex]\dfrac{a}{b}=0.75[/tex].
