Answer:
Equation is [tex]-8x+4y-12=0[/tex]
Step-by-step explanation:
An equation is a mathematical statement that two things are equal .
A system of equations is a set of two or more equations consisting of same unknowns.
Two equations [tex]a_1x+b_1y+c_1=0\,,\,a_2x+b_2y+c_2=0[/tex] have unique solution if [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]
infinite solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
no solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
Here, given: [tex]-4x+2y=6[/tex]
We can write this equation as [tex]-4x+2y-6=0[/tex]
Take another equation as [tex]-8x+4y-12=0[/tex]
Here, [tex]a_1=-4\,,\,a_2=-8\,,\,b_1=2\,,\,b_2=4\,,\,c_1=-6\,,\,c_2=-12[/tex]
[tex]\frac{a_1}{a_2}=\frac{-4}{-8}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{2}{4}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{-6}{-12}=\frac{1}{2}[/tex]
such that [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
