Question

How do you solve the following system?: `2x +4y =-9 , 2x +y = -2`

Answer 1

`(1/6,-7/3)`

Explanation:

Labelling the equations.

`color(red)(2x)+4y=-9to(1)`

`color(red)(2x)+y=-2to(2)`

Notice that the term `color(red)(2x)` is common to both equations.

Thus, subtracting (2) from (1) will eliminate it leaving an equation in y which we can solve.

`"Subtract "(1)-(2)" term by term"`

`(color(red)(2x-2x))+(4y-y)=(-9-(-2))`

`rArr3y=-`7

divide both sides by 3

`(cancel(3) y)/(cancel(3))=(-7)/3`

`rArry=-7/3`

Substitute this value into either (1) or (2) and solve for x

Substituting in ( 2)

`2x-7/3=-2`

`rArr2x=-2+7/3=1/3`

dividing both sides by 2

`(cancel(2) x)/cancel(2)=(1/3)/2`

`rArrx=1/3xx1/2=1/6`

`rArr(1/6,-7/3)" is the solution"`
graph{(y+2x+2)(y+1/2x+9/4)=0 [-12.66, 12.65, -6.33, 6.33]}