Greetings!
Find the POI.
[tex] \left \{ {{3x+2y=12} \atop {6x+3y=21}} \right. [/tex]
Multiply Equation #1 by 2.
[tex] \left \{ {{2(3x+2y)=2(12)} \atop {6x+3y=21}} \right. [/tex]
[tex] \left \{ {{6x+4y=24} \atop {6x+3y=21}} \right. [/tex]
Eliminate with subtraction.
[tex] \frac{\left \{ {{6x+4y=24} \atop {6x+3y=21}} \right. }{0x+y=3} [/tex]
[tex]y=3[/tex]
Substitute the value of y.
[tex]6x+3y=21[/tex]
[tex]6x+3(3)=21[/tex]
Simplify.
[tex]6x+9=21[/tex]
Add -9 to both sides.
[tex](6x+9)+(-9)=(21)+(-9)[/tex]
[tex]6x=12[/tex]
Divide both sides by 6.
[tex] \frac{6x}{6}= \frac{12}{6} [/tex]
[tex]x=2[/tex]
The Solution/POI is:
[tex](2,3)[/tex]
Hope this helps.
-Benjamin
