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# Eliminating Variables in Equations

Created by
@AudibleFresno2256

• 1
• 2 (correct)
• -3
• 3

• 3
• 2
• 1
• -3 (correct)

• 2 (correct)
• 5
• 1
• 3
• ### What value does equation 2 (4x + 2y = 28) need to be multiplied by to eliminate the y-terms?

<p>5</p> Signup and view all the answers

### What is the solution for the equations x - y = 12 and x + 2y = 21?

<p>(15, 3)</p> Signup and view all the answers

### What is the solution for the equations 3x + 4y = -3 and 5x + 3y = 6?

<p>(3, -3)</p> Signup and view all the answers

### Construct the equations for the statement: The sum of two numbers is 21, and their difference is 9. Equation 1: ______ and Equation 2: ______

<p>x + y = 21, x - y = 9</p> Signup and view all the answers

### Construct the equations for the statement: A certain number is three more than five times another number. Their difference is 11. Equation 1: ______ and Equation 2: ______

<p>x = 5y + 3, x - y = 11</p> Signup and view all the answers

### How many adult tickets were sold if 200 tickets were sold for $475, with student tickets at$2 each and adult tickets at $3 each? <p>75 Adult Tickets</p> Signup and view all the answers ## Study Notes ### Eliminating Variables in Equations • To eliminate x-terms in the system consisting of 6x − 5y = -4 and 4x + 2y = 28, multiply Equation 1 by 2 and Equation 2 by -3. • This results in 12x - 10y = -8 and -12x - 6y = -84, effectively cancelling the x-values. ### Eliminating y-terms in Equations • To eliminate y-terms in the same equations, multiply Equation 1 by 2 and Equation 2 by 5. • The resulting equations are 12x - 10y = -8 and 20x + 10y = 140, cancelling the y-values. ### Solving a System of Equations • For the system x − y = 12 and x + 2y = 21, multiply the first equation by 2 to facilitate cancellation of y-values. • Solve for x and substitute back to find y, yielding the solution (15, 3). ### Least Common Multiple in Systems • The system 3x + 4y = -3 and 5x + 3y = 6 requires establishing a least common multiple for the y-values, which is 12. • Multiply the first equation by 3 and the second by 4 to eliminate y, then solve for x and substitute to find y, resulting in the solution (3, -3). ### Constructing Equations from Word Problems • When two numbers sum to 21 and have a difference of 9, the equations are x + y = 21 and x - y = 9. • For the scenario where one number is three more than five times another and their difference is 11, the equations are x = 5y + 3 and x - y = 11. ### Word Problem Involving Ticket Sales • A scenario with 200 total tickets sold for a concert and a total income of$475 leads to the equations x + y = 200 and 2x + 3y = 475.
• Solving for x in the first equation and substituting into the second yields 75 adult tickets sold.

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## Description

This quiz covers methods for eliminating variables in systems of equations, employing techniques such as multiplication and cancellation. It includes examples demonstrating how to solve systems by eliminating x-terms and y-terms. Test your understanding of these crucial algebra concepts.

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