Answer:
The solution is (-2,-11)
Step-by-step explanation:
The given system is ;
[tex]\frac{1+y}{2y} -\frac{3x+1}{y} =0, y\ne0[/tex]
Multiply through by 2y.
[tex]1+y-2(3x+1)=0[/tex]
Expand;
[tex]1+y-6x-2=0[/tex]
[tex]y-6x=1[/tex]
[tex]y=6x+1...(1)[/tex]
Also we have;
[tex]\frac{2y+8}{12x+10}+\frac{4x}{y+7}=3...(2)[/tex]
Put equation (1) into (2)
[tex]\frac{2(6x+1)+8}{12x+10}+\frac{4x}{6x+1+7}=3[/tex]
[tex]\frac{12x+2+8}{12x+10}+\frac{4x}{6x+1+7}=3[/tex]
[tex]\frac{12x+10}{12x+10}+\frac{4x}{6x+8}=3[/tex]
[tex]\frac{12x+10}{12x+10}+\frac{4x}{6x+8}=3[/tex] for [tex]x\ne -\frac{5}{6},x\ne -\frac{4}{3}[/tex]
[tex]1+\frac{4x}{6x+8}=3[/tex]
[tex]\frac{4x}{6x+8}=3-1[/tex]
[tex]\frac{4x}{6x+8}=2[/tex]
Cross multiply;
[tex]4x=2(6x+8)[/tex]
[tex]4x=12x+16[/tex]
[tex]4x-12x=16[/tex]
[tex]-8x=16[/tex]
Divide through by -8.
x=-2
Put x=-2 into equation (1).
y=6(-2)+1
y=-11
The solution is (-2,-11)
