Solve by Elimination
-4x - 2y = -12
4x + 8y = -24
(6,-6)
3x+4y=33
6x+3y=36
(3,6)
y = -3x + 4
y = 3x -2
(1,1)
How many solutions does this system of equations have?
y = -2x - 15
y = x^2 - 2x - 1
No Solutions
A bird dives towards the surface of the water modelled by y = x^2 - 10x + 25. Another bird dives after the first bird along a path modelled by y = -3x + 13. Will the two birds ever collide? If so, when and where?
(3,4) - After 3 seconds, the second bird hits the first, 4 ft above the water
(4,1) - After 4 seconds, the birds hit, 1 foot above the water
-5x + 4y = 20
10x - 8y = -40
2x + 9y = 27
x - 3y = -24
(-9,5)
y = x + 2
x = -3
(-3,-1)
How many solutions does the system of equations have?
y = -2x^2 + 2x + 7
y = x + 3
2 Solutions
Joe and Bekah go to the shop to buy potato chips and candy bars. Joe buys 3 bags of potato chips and 4 candy bars. He spends $3.75. Bekah buys 4 bags of potato chips and 2 candy bars. She spends $3.00. Later, Meg joins Bekah and Joe and asks to buy one bag of potato chips and one candy bar from them. How much does one bag of potato chips cost and how much does one candy bar cost?
(.45, .6)
The potato chips cost $0.45 per bag while the candy bars cost $0.6 per bar.
2x+6y=14
3x-4y=-5
(1,2)
x - 2y = 8
8x + 6y = 42
(6,-1)
x - y = 3
7x - y = -3
(-1, -4)
Solve the system of equations:
y = x^2 + 2x + 5
y = -2x + 1
(-2,5)
Annie wants to order new jerseys for her soccer team. She sees the Company A sells jerseys for $21 each jersey. Company B sells their jerseys with a one-off setting up cost of $45 and then will sell each one after that for $18. When do both companies cost the same?
When Annie is buying 15 jerseys
4x + 3y = 16
2x+2y=4
(10,-8)
2x - 2y = 14
x - y = 2
4 does not equal 14. No solution!
4x + y = 2
x - y =3
(1, -2)
Solve the system of equations:
y = x^2 - 5x -4
y = -2x
(-1,2)
(4,-8)
The length of a rectangle is equal to triple the width. What is the length and width of the rectangle if the perimeter is 86 centimeters?
The length us 32.25 cm and the width is 10.75 cm.
-5x + y = -2
-3x + 6y = -12
(0,-12)
x = 4y
x + 2y = 12
(8,2)
3x - y = -2
2y - 4 = x
(0,2)
Find the solutions to the system of equations:
y=5x-20
y=x^2-5x+5
(5,5)
Beth spent $480 on pairs of pants. Dress pants cost $95 and jeans cost $65. If she bought a total of 6 items, how many of each kind did she buy?
She bought 3 pairs of dress pants and 3 pairs of jeans.