The given system of equations has infinitely many solutions.
Important information:
- [tex]2x-9y=-5[/tex]
- [tex]4x-6y=2[/tex]
System of equations:
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 if [tex]\frac{a_1}{a_2} =\frac{b_1}{b_2} =\frac{c_1}{c_2}[/tex].
In the given equations, [tex]a_1=20,b_1=-9,c_1=-5,a_2=4,b_2=-6,c_2=2[/tex].
[tex]\frac{2}{4} =\frac{-9}{-6} =\frac{-5}{2} =5[/tex]
[tex]\frac{a_1}{a_2} =\frac{b_1}{b_2} =\frac{c_1}{c_2}[/tex], therefore the given system of equationsinfinitely many solutions.
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