Solve each system by substitution. See Example 1.7x - y = -10 3y ...

Question

Solve each system by substitution. See Example 1.7x - y = -10 3y - x = 10

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 five, X minus Y is equal to negative 30. And the second given equation is four, Y minus two, X is equal to 30. Here we have four answers. Choice options, answer choice A no solution answer B X is equal to negative one and Y is equal to one answer. C X is equal to 15 and Y is equal to negative 10 and answer D X is equal to negative five and Y is equal to five. So to use the substitution method, we need to select either of our given equations and solve for either X or Y. So here I'm going to select the second equation and solve for X. So solving for X, we just need to subtract four Y from both sides of the equation to start. And so we have negative two, X is equal to 30 minus four Y. Now we just need to finish solving for X by dividing both sides by its coefficient which is negative two. So we have X is equal to negative 15 plus two Y. And so now using this expression, we found four X, we need to substitute it into our first equation so that we can solve for Y. So substituting in this expression again, we are substituting it into our original equation where we had five X minus Y is equal to negative 30. And now we have five times the quantity of negative 15 plus two Y and then we have minus Y is equal to negative 30. So now we just need to distribute in this five into our expression in the parentheses. And so we have negative 75 plus 10, Y minus Y is equal to negative 30. So now just combining like terms, we have negative 75 plus nine Y is equal to negative 30 30. And now we can simply solve four Y. So first, we just add 75 to both sides of our equation. And so we have nine, Y is equal to 45. Now dividing both sides by the coefficient of Y, we divide both sides by nine and we find that our value for Y is five. So now using this value, we found four Y, we need to substitute it into our equation that we found for X where we had X is equal to negative 15 plus two Y. So doing this, we now have X is equal to negative 15 plus two times the value we found for Y which is five. So now we just need to simplify the product. So we have X is equal to negative 15 plus 10. And now adding these terms, we have X is equal to negative five. So now we have found a value for X and the value for Y. So we are left with answer choice D where again, X is equal to negative five and Y is equal to five. 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 1.7x - y = -10 3y - x = 10

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