Systems of Equations Introduction

Larry and his sister, Betty, are saving money to buy their own laptop computers. Larry has $215 and can save $35 each week. Betty has $380 and can save $20 each week. When will Larry and Betty have the same amount of money? Give the equations and the point of intersection.

• Larry: y = 25x + 215 ; Betty: y = 10x + 380 . The solution is (26, 300). They will both have $300 in 26 weeks.

• Larry: y = 35x + 215 ; Betty: y = 20x + 380 . The solution is (11, 600). They will both have $600 in 11 weeks.

• Larry: y = 15x + 615 ; Betty: y = 65x + 80 . The solution is (10, 1500). They will both have $1500 in 10 weeks.

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

Solve for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

What is the value of the y-coordinate of the solution to the system of equations 
x-2y=1
x+4y=7 

• 1

• -1

• 3

• 4

Solve the following system by setting the two equations equal to each other.  What is the solution?
HINT:  - 1/3x + 4 = 2/3x + 1 and then solve for x.  Once you find x go back and find y.

• Infinite number of solutions

• (3, 3)

• (3, -3)

• (-3, 3)

Solve:
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

2x - y = 0

4x - y = 0

• (1,2)

• (0,0)

• No Solutions

• Infinite Solutions

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions

The equations of two lines are:
 2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?

• x=8

• x=3

• x=11

• x=5