Question 120298
First let's solve the second equation for y

{{{2x=-y}}} Start with the second equation



{{{2x/-1=y}}} Divide both sides by -1 to isolate y



{{{-2x=y}}} Divide 



So our second equation is now:


{{{y=-2x}}}





Which means we have the system 


{{{4x+y=-2}}}

{{{y=-2x}}}





Start with the given system

{{{4x+1y=-2}}}
{{{y=-2x}}}




{{{4x+1(-2x)=-2}}}  Plug in {{{y=-2x}}} into the first equation. In other words, replace each {{{y}}} with {{{-2x}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{4x-2x=-2}}} Multiply



{{{2x=-2}}} Combine like terms on the left side



{{{x=(-2)/(2)}}} Divide both sides by 2 to isolate x




{{{x=-1}}} Divide





Now that we know that {{{x=-1}}}, we can plug this into {{{y=-2x}}} to find {{{y}}}




{{{y=-2(-1)}}} Substitute {{{-1}}} for each {{{x}}}



{{{y=2}}} Simplify



So our answer is {{{x=-1}}} and {{{y=2}}} which also looks like *[Tex \LARGE \left(-1,2\right)]




Notice if we graph the two equations, we can see that their intersection is at (-1,2). So this verifies our answer.



{{{ graph( 500, 500, -5, 5, -5, 5, (-2-4x)/1, -2x) }}} Graph of {{{4x+y=-2}}} (red) and {{{y=-2x}}} (green)