### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# MATH121, Lesson 3.2 Notes Math 121

OleMiss

GPA 3.37

### View Full Document

## 6

## 0

## Popular in College Algebra

## Popular in Math

This 4 page Class Notes was uploaded by Mallory McClurg on Sunday September 18, 2016. The Class Notes belongs to Math 121 at University of Mississippi taught by Dirle in Fall 2016. Since its upload, it has received 6 views. For similar materials see College Algebra in Math at University of Mississippi.

## Reviews for MATH121, Lesson 3.2 Notes

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/18/16

Math121 Chapter 3 Lesson 3.2 – Linear Equations in Two Variables EXAMPLE 1. -2x + 11(x + 2y) = 11x + y (When solving linear equations with two variables, we want to get it in the proper form ax + bx = c. If we cannot get it into this form, it is not linear! Simple enough, right? So first, distribute the 11 to the x and 2y.) -2x + 11x + 22y = 11x + y (Now combine like terms.) 9x + 22y = 11x + y (Now, subtract the terms with variables on the right side of the equation from the left side of the equation to get it in the proper form.) -2x + 21y = 0 (Yes! It’s linear. Yay.) EXAMPLE 2. (y + 3) – y = -5x + 1 (First, factor out the (y + 3) .) y + 6y + 9 – y = -5x + 1 (Now, combine like terms on like sides of the equation.) 6y + 9 = -5x + 1 (Subtract terms with variables on the right side of the equation from the left side of the equation.) 6y + 5x = -8 (Yes! It’s linear, because this is in proper form.) EXAMPLE 3. 2 2 2 8x – (x + 1) = y – 2 (First, factor out the (x + 1) .) 8x – (x +2x + 1) = y – 2 (Take away the parentheses from the quadratic, and change the signs to simplify the lef2 side of the equation.) 7x – 2x – 1 = y – 2 (Subtract terms with variables on the right side of the equation form the left side of the equation.) 2 7x – 2x – y + 1 = 0 (This is not in proper form; NOT LINEAR.) EXAMPLE 4. x + 3xy = 4y (Can we simplify this to put it in proper form? No….. NOT LINEAR.) EXAMPLE 5. (11/x) + (7/y) = 6 (Can we simplify this to put it in proper form? No… NOT LINEAR.) Math121 Chapter 3 EXAMPLE 6. (11x – y)/2 + 3y = 8 (Separate the (11x – y)/2 into two fractions.) (11x/2) – (y/2) + 3y = 8 (To combine the terms on the left side of the equation with like variables, we need to turn 3y into a fraction with 2 as the denominator. So multiply the fraction (3y/1) by (2/2).) (11x/2) – (y/2) + (6y/2) = 8 (Now, combine fractions with like terms and put it in proper ax + by = c form.) (11/2)x – (5/2)y = 8 (This is in proper LINEAR form!) EXAMPLE 7. 3x + 7y = -21 (We are asked to find all x and y intercepts in this linear equation. Since we know that an x intercept has a y value of y = 0, and a y intercept has an x value of x = 0, we can find each intercept by writing two equations, with x = 0 in one, and y = 0 in the other.) 3(0) + 7y = -21 3x + 7(0) = -21 7y = -21 3x = -21 y = -3 x = -7 (0, -3) (-7, 0) EXAMPLE 8. 5y – 4x = -20 (To find the intercepts, let y = 0 in one equation and x = 0 in the other, because we know they intercept the axes where the value is zero.) 5(0) – 4x = -20 5y – 4(0) = -20 -4x = -20 5y = -20 x = 5 y = -4 (5, 0) (0, -4) EXAMPLE 9. -2y + 3x = -2y + 6 (We need to put this in proper ax + by = c form, so add 2y to both sides of the equation.) Math121 Chapter 3 3x = 6 (The terms with y as a variable both cancelled each other out…, so the y intercept value is absent.) x = 2 (2, 0) (y is absent) EXAMPLE 10. -6y = - 48 (The x variable is absent, so solve for the value of y.) y = 8 (0, 8) (x is absent) EXAMPLE 11. -3x = -3y (If we divide both sides by -3, we see that it’s y = x.) x = y (In this situation, we should realize that this means x = 0 (0, 0) and y = 0 (0, 0).) Math121 Chapter 3 EXAMPLE 12. 8x + 14 = -8y + 14 (Subtract 14 from both sides.) 8x = -8y (Divide both sides by -8.) -x = y EXAMPLE 13. 7y – 7 = 2x (Get this in ax + by = c form.) -2x + 7y = 7 (In two separate equations, let x = 0 in one, and y = 0 in the other to find the intercepts.) -2(0) + 7y = 7 -2x + 7(0) = 7 7y = 7 -2x = 7 y = 1 x = (-7/2) (0, 1) (-7/2, 0) EXAMPLE 14. 8 – 2y = 28 – 5x (Write out into two equations, trying to get the y on a side by itself in one, and the x on a side by itself in the other.) -2y = 20 – 5x -20 – 2y = -5x y = -10 – (5/-2)x x = 4 – (2/-5)y (Now, set each equal to zero to find the x and y intercepts.) (5/2)x – 10 = 0 (2/5)y + 4 = 0 10 = (5/2)x -4 = (2/5)y x = 4 y = -10 (4, 0) (0, -10)

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I made $350 in just two days after posting my first study guide."

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.