Answer:
Infinitely many solutions.
Step-by-step explanation:
Given
[tex]3x-2y=12\\ 6x-4y=24[/tex]
Required;
Find the solution
[tex]3x-2y=12 --(1)\\ 6x-4y=24 -- (2)[/tex]
Make x the subject of formula in (1)
[tex]3x-2y=12[/tex]
Add 2y to both sides
[tex]3x-2y+2y=12+2y[/tex]
[tex]3x=12+2y[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{12+2y}{3}[/tex]
[tex]x=\frac{12+2y}{3}[/tex]
Substitute [tex]x=\frac{12+2y}{3}[/tex] in (2)
[tex]6x-4y=24[/tex]
[tex]6(\frac{12+2y}{3})-4y=24[/tex]
[tex]2(12+2y)-4y=24[/tex]
Open Bracket
[tex]24+4y-4y=24[/tex]
[tex]24+4y-4y=24[/tex]
Collect Like Terms
[tex]4y-4y=24-24[/tex]
[tex]0 = 0[/tex]
Based on the result above, the two equations have infinitely many solutions.
