In Exercises 43–46, let x represent one number and let y represen...

Question

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.

Accepted Answer

Welcome back. I am so glad you're here. We are given a set of circumstances and we are asked to create a system of equations for that and then solve for our variables. The variables were asked to use our X and Y. So our circumstances we've got to for the first set of circumstances we're told that the addition of the first number. Okay, so equation one, we're adding the first number, that could be X and double of the other number will double the other number is why? So we can double that. We say to y Is is as equals 22. And there is how we set up the first equation. The second equation. The difference between these two numbers. Well, that means we're going to subtract them and it's just these two numbers. So it's X minus Y Is or equals -2. Okay, there's our second equation. Now. We just need to solve them. Using what we recall from previous lessons on solving for systems of equations. I am going to use the addition method and I'm going to take the first equation, multiplied by negative one, add that to the second equation and our x terms will cancel out and we can solve for y. So negative one times X is negative X negative one times two, Y is minus two, Y equals 22 times negative one is negative adding these two equations together. The x's cancel out negative y minus two, Y is negative three, Y equals negative two minus 22 is negative 24 Dividing both sides by -3 and we have Y equals negative 24 divided by negative three is a positive eight. Why equals eight. Now we can take Y equals eight and we can substitute this eight and for Y and I'll do that in the second equation. So now it's X minus not Why, but eight equals -2, adding eight to both sides to get X by itself, we get X equals negative two plus eight is a positive six. And so we have solved for X and for Y, we look at our solution sets and this matches with answer choice A Well done, we'll catch on the next one.

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.

Key Concepts

System of Equations

Linear Equations

Substitution and Elimination Methods

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