Question

Solve each system of equations by writing a new system that eliminates one of the variables.

2x+y=25
4x+3y=9

Answer 1

`x=33\\y=-41`

Explanation:

Let:

`2x+y=25\hspace{5}(1)\\and\\4x+3y=9\hspace{5}(2)`

We need to eliminate one of the variables, so let's use elimination method. First multiply (1) by 2

`2*(1)\equiv\hspace{5}4x+2y=50`

Now subtract (2) from 2*(1) in order to eliminate x:

`2*(1)-(2)\\4x-4x+2y-3y=50-9\\-y=41`

Solving for y:

Multiplying both sides by -1

`y=-41`

Finally, replacing the value of y in (1)

`2x-41=25`

Solving for x:

add 41 to both sides:

`2x=66`

Multiply both sides by 1/2:

`x=(66)/(2) =33`