Question

What is the solution of the system?

Use the elimination method.

{4x+2y=182x+3y=15

Answer 1

x=15-3y
4(15-3y)+2y=182
60-12y+2y=182
-10y=182-60
-10y=122
-y=122/10
-y=12.2
y=-12.2
x=15--3(12.2)=51.6

Answer 2

`x=3` and
`y=3`

Explanation:

The system of equations:

`4x+2y=18\\2x+3y=15`

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:

`2(2x+3y=15)\\4x+6y=30`

and subtracting this from the first equation:

`4x+2y=18\\-(4x+6y=30)`

which is:

`4x+2y=18\\-4x-6y=-30`

this gives the following:

`4x+2x-4x-6y=18-30\\-4y=-12\\y=(-12)/(-4) \\y=3`

We just eliminated the variable
`x` to find
`y`. Finally we substitute the value of
`y=3` in any of the equations to find
`x`.

using
`4x+2y=18`

`4x+2(3)=18\\4x+6=18\\4x=18-6\\4x=12\\x=3`

the solution is
`x=3` and
`y=3`