Solve the system by the substitution method. x^2 + y^2 =...

Solve the system by the substitution method. x^2 + y^2 = 109 x - y = -7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { }. (Type an ordered pair. Use a comma to separate answers as needed.) B. There is no solution. Click to select and enter your answer(s) and then click Check Answer.

Transcript

00:01 Have these two equations x square plus y square equals one and nine and x minus y equals seven so the first one is equation one second is equation two so from equation two i say x equals seven plus y we make equation three so substitute the value of equation three into equation one right so that'll be seven plus y rise part two plus y square equals one zero nine so when you expand you get 49 plus seven y plus seven y plus y plus y square because one and nine so that leads us with y square plus 14 by this is added then i'll take minus 109 to the other side becomes minus 49 minus 109 that will leave us with minus 60 which is what i have here so when you factorize look for two numbers such that when you had you get 14 and then when you multiply the two numbers you get minus 60 so we then have y cost 3 .4 4 when you go by pythagra your quadratic formula minus b plus or minus squared of b squared minus 4 is over 2a b in this case is 14 coefficient of c is minus 60 question of a is 1 so therefore you have a squared of this gives us 20 288 minus 14 plus or minus 20 .88 over 2 becomes you see that you have in this case plus minus 14 plus 20 .80 divided by 2 that 6 .80 divided by 2 that 6 .80 divided by 2 or when minus 14 minus 20 .80 divided by 2 you have minus 17 .44.

01:37 So let's go back to the original equation that says one of the equations here.

01:42 Equation 2 x minus y.

01:46 X minus y equals 7.

01:49 Yeah x minus y equals 7.

01:51 So we'll say that x when y is 3 .4.

01:57 So x is going to be, um, x is going to be you take it to the other side.

02:02 That will 10 .44 so we have 10 .44...

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