Systems ofEquations

Ax+By=C to y = mx+b

InterceptsVerify

Solutions Writing

Equations

Q $100

Q $200

Q $300

Q $400

Q $500

Q $100 Q $100Q $100 Q $100

Q $200 Q $200 Q $200 Q $200

Q $300 Q $300 Q $300 Q $300

Q $400 Q $400 Q $400 Q $400

Q $500 Q $500 Q $500 Q $500

Final Jeopardy

What is the solution to this system of equations?

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3 3

7

y x

y x

(1,6)

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A system of equations has been graphed at the right. What is the solution to this system of equations?

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(4,3)

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What is the solution of the system of equations: x + y = 5

x - y = 3

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(4, 1)

What is the solution of the system of equations: 2x – 5y = 11

-2x + 3y = - 9

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(3, - 1)

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You want to use the elimination method to solve for the solution to this system of equations.

3 7 8

5 8 6

x y

x y

Describe how you can eliminate the y term.

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Multiply the first equation by -8 and the second equation by 7 and then add the equations.

Or

Multiply the first equation by 8 and the second equation by -7 and then add the equations

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Given the system of equations, what do you know about the solution?

3 2

6 2

y x

y x

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There is no solution—The lines are parallel—They lines will not intersect

What is the y-intercept of the graph of 4 x + 2 y = 12 ?

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y-intercept is6or

(0, 6)

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What is the slope of the graph of 4 x + 2 y = 12 ?

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Slope is -2 or -2/1

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Rewrite the equation below into slope-intercept form.

3x + 2y = 6

y = 3 – 3/2xor

y = -3/2x + 3

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Rewrite the equation below into slope-intercept form.

-x – 6y = - 12

y = 2 – 1/6xor

y = -1/6x + 2

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What is the equation that represents the graph below?

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y = 2 – 2/3xor

y = -2/3x + 2

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What are the x & y intercepts for the graph below?

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X-intercept = -1 or (-1, 0)

Y-intercept = - 2 or (0, -2)

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What are the x & y intercepts for the equation:

4x + 2y = 12

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X-intercept is 3 or (3, 0)Y-intercept is 6 or (0, 6)

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What are the x & y intercepts for the equation:

3x – y = 9

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X-intercept is 3 or (3, 0)Y-intercept is -9 or (0, -9)

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A pet store sells angel fish for $6 each and clown fish for $4 each. It sold $36 worth of fish.

How many angel fish would be sold if 0 clown fish were sold?How many clown fish would be sold if 0 angel fish were sold?

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6 angel fish and 0 clown fish

0 angel fish and 9 clown fish

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Which equation represents the graph below?  A 2x – y = -2B 2x + y = -2C x – 2y = -2D -x + 2y = -2

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B) 2x + y = -2

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Is (2,1) a point on the line defined by 3x + 6y = 12?

Must show work!

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YES!!3x + 6y = 12

3(2) + 6(1) = 126 + 6 = 12

12 = 12

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Is (1, -7) a solution to the system of equations?-3x + y = - 2x + y = - 6

You must show your work!

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No-3x + y = - 2

-3(1) + -7 ≠ -2-3 + -7 ≠ -2

-10 ≠ -2

Is (-1, -5) a solution to the system of equations?

-3x + y = - 2x + y = - 6

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YES! The point (-1, -5) worked for BOTH equations

-3x + y = -2 x + y = - 6-3(-1) + -5 = -2 -1 + -5 = - 6 3 + -5 = -2 - 6 = - 6 -2 = -2

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For what value of x is (x, - 3) a solution for 4x – 3y = 21? A) -11B) -3C) 3D) 11

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C) 3

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(1, 2) is a solution to which system of equations?

a) 2x + y = 4 -x + y = 3

b) -4x + y = - 4 6x + y = 8

c) -x + y = 1 x + y = 3

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c) -x + y = 1 -(1) + 2 = 1 x + y = 3 1 + 2 = 3

Tyheim paid $17.50 to buy 6 youth tickets and 1 adult ticket to a school carnival. Ashley paid $22.50 to buy 3 youth tickets and 3 adult tickets at the carnival.

Write a system of equations to represent the situation. (Let x represent cost of youth ticket and y represent cost of adult ticket)

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Tyheim’s Equation 6x + y = 17.50Ashley’s Equation 3x + 3y = 22.50

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Tickets for a school concert cost $2 for students and $5 for adults. A total of 200 tickets were sold for $670. Write a system of equations to represent the situation.

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2x + 5y = 670 x + y = 200

The Arcadia Theater charges $4 for adult tickets and $3 for student tickets. Mr. Steele purchased 9 tickets (some student and some adult) for $31. Which system of equations could be used to find a, the number of adult tickets, and s, the number of student tickets Mr. Steele purchased?

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Billy had a total of $47 in $5 and $1 bills in his wallet. He had a total of 15 bills. Write a system of equations that represents the situation if x represents $5 bills and y represents $1 bills?

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5x + y = 47 x + y = 15

The only coins Alex has are dimes and quarters.

•His coins have a total value of $5.80.•He has a total of 40 coins.

Write a systems of equations that can be used to find the number of dimes, d, and the number of quarters, q, that Alex has?

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.10d + .25q = 5.80 d + q = 40

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Complete the following statements:

1.A system of two linear equations has no solution if …2.A system of two linear equations has infinitely many solutions if …3.A system of two linear equations has exactly one solution if …

1. The equations have different y-intercepts and the same slope (parallel lines)

2. The equations have the same y-intercept and the same slope (same lines)

3. The equations have different slopes (intersecting lines)

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