Question 197997
"A first number plus twice a second number is 5. Twice the first number plus the second totals 4" translates to the system: {{{system(x+2y=5,2x+y=4)}}}




Start with the given system of equations:

{{{system(x+2y=5,2x+y=4)}}}



{{{-2(x+2y)=-2(5)}}} Multiply the both sides of the first equation by -2.



{{{-2x-4y=-10}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-2x-4y=-10,2x+y=4)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(-2x-4y)+(2x+y)=(-10)+(4)}}}



{{{(-2x+2x)+(-4y+1y)=-10+4}}} Group like terms.



{{{0x+-3y=-6}}} Combine like terms.



{{{-3y=-6}}} Simplify.



{{{y=(-6)/(-3)}}} Divide both sides by {{{-3}}} to isolate {{{y}}}.



{{{y=2}}} Reduce.



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



{{{-2x-4y=-10}}} Now go back to the first equation.



{{{-2x-4(2)=-10}}} Plug in {{{y=2}}}.



{{{-2x-8=-10}}} Multiply.



{{{-2x=-10+8}}} Add {{{8}}} to both sides.



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



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



{{{x=1}}} Reduce.



So the solutions are {{{x=1}}} and {{{y=2}}}.



which means that the first number is 1 and the second number is 2