Solve each system by substitution. See Example 1. 4x + 3y = -13-x...

Question

Solve each system by substitution. See Example 1. 4x + 3y = -13-x + y = 5

Accepted Answer

Hey, everyone. Here we are asked to use the substitution method to solve the given system of equations where the first equation is two X plus five, Y is equal to negative 11. And the second equation is negative X plus Y is equal to nine. Here we have four answer choice options. Answer A X is equal to negative A and Y is equal to negative one answer B X is equal to negative one and Y is equal to eight answer C X is equal to negative A and Y is equal to one and answer D no solution. So to use the substitution method, we first need to solve one of our given equations for either X or Y. So here we can select our second equation and we can see that we can easily solve for Y by simply adding X to both sides of the equation. And so we find that Y is equal to nine plus X. And now we take this expression, we found four Y and substitute it into our first equation so that we can solve four X. So instead of having two X plus five Y is equal to negative 11, we now have two X plus five times the quantity of nine plus X is equal to negative 11. So now the next step is to just substitute in this or distribute in this five into our expression. So we have two X plus 45 plus five X is equal to negative 11. Now just combining like terms two X plus five X gives us seven X plus 45 is equal to negative 11. Now just solving for X, we first need to get XX alone by just subtracting 45 from both sides of the equation. So we have seven X is equal to negative 56. Now, the last step in solving four X is to divide by its coefficient. So we divide both of both sides of our equation by seven. And so we are left with X being equal to negative eight. And now we take this value for X that we found and substitute it into our expression, we found four Y. So instead of having Y is equal to nine plus X, we now have Y is equal to nine plus our value for X which is negative eight. Now just simplifying nine plus negative eight gives us one. So we find that Y is equal to one. So here we found our value for Y and our value for X. So we are left with answer choice C where X is equal to negative eight and Y is equal to one. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Struggling with College Algebra?

Solve each system by substitution. See Example 1. 4x + 3y = -13-x + y = 5

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