Question 841149

Solve using either the substitution method or the addition method.


6x+3y=0 
8x+5y=8 


---------------------------------------------
1.) I'm going to label the equations so I can reference back to them.



Equation 1.) {{{6x+3y=0}}}
Equation 2.) {{{8x+5y=8}}}


---------------------------------------------
2.) I'm going to use the substitution method. Get "y" by itself in equation 1.



Equation 1.) 


{{{6x+3y=0}}}


{{{6x-6x+3y=0-6x}}}


{{{3y=-6x}}}


{{{3y/3=-6x/3}}}


{{{y=-2x}}}


--------------------------------------------
3.) Now using {{{y=-2x}}}, plug in to equation 1 or equation 2. Solve for "x".


Equation 2.) 

{{{8x+5y=8}}}

{{{8x+5(-2x)=8}}}

{{{8x-10x=8}}}

{{{-2x=8}}}


{{{(-2x)/-2=8/-2}}}

{{{x=-4}}}


-----------------------------------------
4.) Use either equation 1 or equation 2 and plug in {{{x=-4}}}. Solve for "y".


Equation 2.) 

{{{8x+5y=8}}}

{{{8(-4)+5y=8}}}


{{{-32+5y=8}}}

{{{-32+32+5y=8+32}}}

{{{5y=40}}}


{{{5y/5=40/5}}}

{{{y=8}}}


------------------------------------------
5.) Check that {{{x=-4}}} and {{{y=8}}} for either equation 1 or equation 2.


***Note I'm going to show that both check.


Equation 1.) 

{{{6x+3y=0}}}

{{{6(-4)+3(8)=0}}}

{{{-24+24=0}}}

{{{0=0}}}


Checks!


-------------------


Equation 2.) 

{{{8x+5y=8}}}

{{{8(-4)+5(8)=8}}}

{{{-32+40=8}}}

{{{8=8}}}


Checks!


------------------------------------------------------
6.) Answer.


{{{x=-4}}}

{{{y=8}}}