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# Mathcounts- System of Equations

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Tweet## Teja Veerati

on 14 October 2012#### Transcript of Mathcounts- System of Equations

By Teja Veerati System of Equations Last week, we talked about variables and equations and how to solve them. System of equations is the same concept. The only difference is that you're solving for multiple variables using multiple equations. What is a system of equations? A store sells apples for 50 cents each and oranges for 75 cents. If Sara spends $12. 75 to buy 21 fruits, how many apples and oranges did she buy? Example How to solve:

1. This is a system of equations problem since we are solving for 2 variables.

2. Write the equations using the given information.

3. Solve the equations.

substitution

canceling

4. ALWAYS plug answers back into the equation and check. One important thing to remember about system of equations is that you always have the same number of equations as you do unknown values. By solving all the equations, you can determine the unknowns. How to solve system of equations? 2 methods:

- substitution

- elimination Substiution Example 1

3x + 2y= 5

x + 5y= 6 Elimination Example 2

4x + 2y= 14

-3x + y= 2 Review of last week But no matter what method you chose, the basic idea is that you solve for one variable, and then plug it in to the other equation and solve for the other variable.

And make sure you ALWAYS plug in your answers and check!!!! 1. The sum of two numbers is 20, and their difference is 8, what are they? Practice with Word Problems 2.The sum of two numbers is 1/3, and their difference is 1/6, what are they? 3.The sum of two numbers is 1/6, and their difference is 1/3, what are they? 4.Madison has 52 coins in quarters and nickels, amounting to $10. How many nickels does she have? The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended? More Practice The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number. Practice 5x + y = 9

10x 7y = 18 x=1

y=4 −x − 7y = 14

−4x − 14y = 28 x=0

y= -2 3x − 2y = 2

5x − 5y = 10 x= -2

y= -4 5x + 4y = −14

3x + 6y = 6 x= -6

y= 4 Real SAT Problems If x^2 - y^2 = 77, and x+y= 11, what is value of x? Answer

x=9 If 2r=5s and 5s=6t, what does r equal in terms of t?

(A) 12t/25

(B) 6t/5

(C) 3t

(D) 15t

(E) 30t Answer:

C If x-y=8, y=3z, and z=2, what is the value of x?

(A) -14

(B) -2

(C) 2

(D) 3

(E) 14 Answer:

E A school ordered $600 worth of lightbulbs. Some of the lightbulbs cost $1 each and the others cost $2 each. If twice as many $1 bulbs as $2 bulbs were ordered, how many lightbulbs were ordered altogether? Answer:

450 Practice Time!!! What were the 3 most important things we learned last week?

Full transcript1. This is a system of equations problem since we are solving for 2 variables.

2. Write the equations using the given information.

3. Solve the equations.

substitution

canceling

4. ALWAYS plug answers back into the equation and check. One important thing to remember about system of equations is that you always have the same number of equations as you do unknown values. By solving all the equations, you can determine the unknowns. How to solve system of equations? 2 methods:

- substitution

- elimination Substiution Example 1

3x + 2y= 5

x + 5y= 6 Elimination Example 2

4x + 2y= 14

-3x + y= 2 Review of last week But no matter what method you chose, the basic idea is that you solve for one variable, and then plug it in to the other equation and solve for the other variable.

And make sure you ALWAYS plug in your answers and check!!!! 1. The sum of two numbers is 20, and their difference is 8, what are they? Practice with Word Problems 2.The sum of two numbers is 1/3, and their difference is 1/6, what are they? 3.The sum of two numbers is 1/6, and their difference is 1/3, what are they? 4.Madison has 52 coins in quarters and nickels, amounting to $10. How many nickels does she have? The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended? More Practice The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number. Practice 5x + y = 9

10x 7y = 18 x=1

y=4 −x − 7y = 14

−4x − 14y = 28 x=0

y= -2 3x − 2y = 2

5x − 5y = 10 x= -2

y= -4 5x + 4y = −14

3x + 6y = 6 x= -6

y= 4 Real SAT Problems If x^2 - y^2 = 77, and x+y= 11, what is value of x? Answer

x=9 If 2r=5s and 5s=6t, what does r equal in terms of t?

(A) 12t/25

(B) 6t/5

(C) 3t

(D) 15t

(E) 30t Answer:

C If x-y=8, y=3z, and z=2, what is the value of x?

(A) -14

(B) -2

(C) 2

(D) 3

(E) 14 Answer:

E A school ordered $600 worth of lightbulbs. Some of the lightbulbs cost $1 each and the others cost $2 each. If twice as many $1 bulbs as $2 bulbs were ordered, how many lightbulbs were ordered altogether? Answer:

450 Practice Time!!! What were the 3 most important things we learned last week?