Answer:
[tex]x=3[/tex] and [tex]y=3[/tex]
Step-by-step explanation:
The system of equations:
[tex]4x+2y=18\\2x+3y=15[/tex]
Using the elimination methos, i want to eliminate the x first. for this, we multiply the second equation by 2, and then we subtract it from the first equation.
Multiplying the second equation by 2:
[tex]2(2x+3y=15)\\4x+6y=30[/tex]
and subtracting this from the first equation:
[tex]4x+2y=18\\-(4x+6y=30)[/tex]
which is:
[tex]4x+2y=18\\-4x-6y=-30[/tex]
this gives the following:
[tex]4x+2x-4x-6y=18-30\\-4y=-12\\y=\frac{-12}{-4} \\y=3[/tex]
We just eliminated the variable [tex]x[/tex] to find [tex]y[/tex]. Finally we substitute the value of [tex]y=3[/tex] in any of the equations to find [tex]x[/tex].
using [tex]4x+2y=18[/tex]
[tex]4x+2(3)=18\\4x+6=18\\4x=18-6\\4x=12\\x=3[/tex]
the solution is [tex]x=3[/tex] and [tex]y=3[/tex]
