Greetings!
Solve the System, using Elimination:
[tex] \left \{ {{4x+2y=18} \atop {2x+3y=15}} \right. [/tex]
Multiply Equation #2 by 2:
[tex] \left \{ {{4x+2y=18} \atop {2(2x+3y)=2(15)}} \right. [/tex]
[tex] \left \{ {{4x+2y=18} \atop {4x+6y=30}} \right. [/tex]
Eliminate variable x:
[tex]-\frac{ \left \{ {{4x+2y=18} \atop {4x+6y=30}} \right.}{0x-4y=-12} [/tex]
[tex]4y=-12[/tex]
Divide both sides by 4:
[tex] \frac{4y}{4}= \frac{12}{4} [/tex]
[tex]y=3[/tex]
Input this value into one of the Equations:
[tex]4x+2y=18[/tex]
[tex]4x+2(3)=18[/tex]
Simplify:
[tex]4x+6=18[/tex]
[tex](4x+6)+(-6)=(18)+(-6)[/tex]
[tex]4x=12[/tex]
Divide both sides by 4.
[tex] \frac{4x}{4}= \frac{12}{4} [/tex]
[tex]x=3[/tex]
The Solution to this System (The Point of Intersection):
[tex]\boxed{(3,3)} [/tex]
I hope this helped!
-Benjamin
