Question 1022398
It's not the correct answer. You can check by going back to the original equations and plugging in the (x,y) solution point. It makes the first equation true, but the second equation is false when you replace x with 2 and y with -1/2


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Here is one way to solve the system



Step 1) Solve {{{x+2y=1}}} for x


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


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


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


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Step 2) Move onto the second equation. Replace every copy of 'x' with '1-2y'


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


{{{-2(1-2y)+y=-4}}} Replaced x with 1-2y


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


{{{-2+5y = -4}}}


Notice how x is gone now. There is only one variable left. Let's solve for y



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Step 3) Solve for y



{{{-2+5y = -4}}}


{{{-2+5y+2 = -4+2}}}


{{{5y = -2}}}


{{{5y/5 = -2/5}}}


{{{y = -2/5}}}


{{{y = -0.4}}}



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Step 4) We'll use this value of y to find x



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


{{{x = 1-2(-0.4)}}} Replaced y with -0.4


{{{x = 1+0.8}}}


{{{x = 1.8}}}



The solution to the system of equations is (x,y) = <font color=red>(1.8, -0.4)</font>



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Let's check the answer



Checking the first equation
{{{x+2y=1}}}
{{{1.8+2*(-0.4)=1}}} Replaced (x,y) with <font color=red>(1.8, -0.4)</font>
{{{1.8-0.8=1}}}
{{{1=1}}}


Checking the second equation
{{{-2x+y=-4}}}
{{{-2*(1.8)+(-0.4)=-4}}} Replaced (x,y) with <font color=red>(1.8, -0.4)</font>
{{{-3.6-0.4=-4}}}
{{{-4=-4}}}



Since BOTH equations are true, this confirms the solution <font color=red>(1.8, -0.4)</font>